Introduction to Management Science A Modeling 6e TB by TestbankMall

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 1 Introduction 1) Managers need to know the mathematical theory behind the techniques of management science so that they can lead management science teams. 2) Management scientists use mathematical techniques to make decisions, which are then implemented by managers. 3) Spreadsheets allow many managers to conduct their own analyses in management science studies. 4) Managers must rely on management science experts to create and understand managerial problems. 5) Management science is a discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors. 6) The discovery of the simplex method in 1947 was the beginning of management science as a discipline. 7) The rapid growth of computing capability and power has led to a corresponding rapid growth of the management science discipline. 8) Managers make decisions based solely on the quantitative factors involved in the problem. 9) A management science team will try to conduct a systematic investigation of a problem that includes careful data gathering, developing and testing hypotheses, and then applying sound logic in the analysis. 10) The mathematical model of a business problem is the system of equations and related mathematical expressions that describes the essence of the problem. 11) A mathematical model of a business problem allows a manager to evaluate both quantitative and qualitative aspects of the problem. 12) Once management makes its decisions, the management science team typically is finished with its involvement in the problem. 13) A cost that varies with the production volume would be a fixed cost. 14) A cost that varies with the production volume would be a variable cost. 15) A cost that does not vary with the production volume would be a fixed cost. 16) A cost that does not vary with the production volume would be a variable cost.

17) At the break-even point, management is indifferent between producing a product and not producing it. 18) The best way to solve a break-even problem with a spreadsheet model is to try different production quantities until the quantity that leads to profits of zero is found. 19) A constraint is an algebraic variable that represents a quantifiable decision to be made. 20) A decision variable is an algebraic variable that represents a quantifiable decision to be made. 21) A parameter in a model is a variable that represents a decision to be made. 22) The objective function for a model is a mathematical expression of the measure of performance for the problem in terms of the decision variables. 23) Sensitivity analysis is used to check the effect of changes in the model. 24) Investigating the potential outcomes when estimates turn out to be incorrect is known as "what-if analysis." 25) "What-if analysis" is a process used to generate estimates for use in mathematical models. 26) Enlightened future managers should know which of the following? A) The power and relevance of management science. B) When management science can and cannot be applied. C) How to apply the major techniques of management science. D) How to interpret the results of a management science study. E) All of the answer choices are correct. 27) The rapid development of the management science discipline can be credited in part to: A) World War I. B) George Dantzig. C) the computer revolution. D) George Dantzig and the computer revolution. E) World War I, George Dantzig, and the computer revolution. 28) Managers may base their decisions on which of the following? A) Quantitative factors. B) Their best judgment. C) Opinions from other managers. D) Past experience. E) All of the answer choices are correct.

29) Management science is based strongly on which of the following fields? A) Mathematics. B) Computer science. C) Business administration. D) Mathematics and computer science only. E) All of the answer choices are correct. 30) Which of the following are components of a mathematical model for decision making? A) Decision variables. B) An objective function. C) Constraints. D) Parameters. E) All of the answer choices are correct. 31) Which of the following are steps in a typical management science study? A) Define the problem and gather data. B) Formulate a model to represent the problem. C) Test the model and refine it as needed. D) Help to implement the recommendations. E) All of the answer choices are correct. 32) Which of the following is a mathematical expression that gives the measure of performance for the problem? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. 33) Which of the following is a constant in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. 34) Which of the following is an inequality or equation that expresses a restriction in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct.

35) A manager has determined that a potential new product can be sold at a price of $10.00 each. The cost to produce the product is $5.00, but the equipment necessary for production must be leased for $25,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. 36) In order to produce a new product, a firm must lease equipment at a cost of $10,000 per year. The managers feel that they can sell 5,000 units per year at a price of $7.50. What is the highest variable cost that will allow the firm to at least break even on this project? A) $2.50. B) $3.50. C) $4.50. D) $5.50. E) $6.50. 37) A manager has determined that a potential new product can be sold at a price of $20.00 each. The cost to produce the product is $10.00, but the equipment necessary for production must be leased for $75,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. 38) Production has indicated that they can produce widgets at a cost of $4.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 4,000 units at $5.00 each. B) 3,000 units at $7.50 each. C) 1,500 units at $10.00 each. D) 1,000 units at $15.00 each E) 25,000 units. 39) A manager has determined that a potential new product can be sold at a price of $50.00 each. The cost to produce the product is $35.00, but the equipment necessary for production must be leased for $100,000 per year. What is the break-even point? A) 3,333 units. B) 5,000 units. C) 6,667 units. D) 7,500 units. E) 8,167 units.

40) In order to produce a new product, a firm must lease equipment at a cost of $25,000 per year. The managers feel that they can sell 10,000 units per year at a price of $15.00. What is the highest variable cost that will allow the firm to at least break even on this project? A) $12.50. B) $13.50. C) $14.50. D) $15.50. E) $16.50. 41) A manager has determined that a potential new product can be sold at a price of $100.00 each. The cost to produce the product is $75.00, but the equipment necessary for production must be leased for $175,000 per year. What is the break-even point? A) 3,000 units. B) 5,000 units. C) 7,000 units. D) 10,000 units. E) 25,000 units. 42) Production has indicated that they can produce widgets at a cost of $3.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 7,500 units at $17.50 each. B) 4,000 units at $20.00 each. C) 3,000 units at $22.50 each. D) 2,500 units at $25.00 each E) 1,500 units at $27.50 each. 43) When evaluating a project to determine the break-even quantity, the advantage of a spreadsheet model is? A) Users can't see the formulas used. B) Calculations are always rounded to the nearest integer. C) The analyst can use Excel's "BREAKEVEN" function to perform the calculation D) A number of different estimates can be quickly evaluated once the model is constructed. E) There are no advantages to spreadsheet modeling of break-even analysis. 44) Which of the following is TRUE about the break-even point? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be negative. C) When sales are below the break-even point, profits will be positive. D) Once sales exceed the break-even point, profits no longer change if sales increase further. E) The total revenue and total cost are equal at the point where profits are maximized.

45) Which of the following statements about the break-even quantity is FALSE? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be positive. C) When sales are below the break-even point, profits will be negative. D) Once sales exceed the break-even point, profits continue to increase as sales increase. E) The total revenue and total cost are equal at the point where profits are maximized. 46) Business analytics is a field which. A) is the same as operations research. B) aids managerial decision making through the use of data. C) uses descriptive analytics to predict the future. D) uses prescriptive analytics to analyze trends. E) uses predictive analytics to determine the best course of action. 47) Descriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. 48) Predictive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. 49) Prescriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. 50) In order to produce a new product, a firm must lease new equipment. The managers feel that they can sell 10,000 units per year at a price of $7.50. If the variable cost of production is $5.00 per unit, what is the most the firm can spend to lease the new equipment without losing money? A) $10,000. B) $15,000. C) $20,000. D) $25,000. E) $30,000.

51) A group is planning a conference. The cost to rent the space is $1,000. Each attendee will be charged $50.00 to attend, but the group provides a lunch (the group will pay $10.00 for each lunch). What is the break-even point? A) 20 attendees. B) 25 attendees. C) 30 attendees. D) 35 attendees. E) 40 attendees. 52) A training firm is planning to offer a one-day class at a local facility. The class is projected to have 50 students, each of whom will pay $25.00 to attend. The firm provides materials to each student (materials cost the firm $10.00 per student). What is the most the firm can afford to pay to rent the facility for one day? A) $250. B) $500. C) $750. D) $1,000. E) $1,250. 53) A tour company is planning a bus trip to a local museum. The company will lease a bus from a local bus owner for $400 and estimates that it will spend $15.00 per person for admission and lunch. Which of the following volume/price alternatives will allow the firm to avoid losing money on the trip? A) 20 customers at $30.00 each. B) 30 customers at $27.50 each. C) 40 customers at $25.00 each. D) 50 customers at $22.50 each E) 60 customers at $20.00 each. 54) You have decided to start a vending machine business. A local store has space available for your machine but wants to charge you an annual fee to use the space. You estimate that you can sell 5,000 cans of soda each year. You sell a can of soda for $1.25, which allows you a profit of $0.50 per can. What is the most you would spend to lease the space for one year? A) $1,000. B) $2,500. C) $5,000. D) $7,500. E) $10,000.

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 1 Introduction 1) Managers need to know the mathematical theory behind the techniques of management science so that they can lead management science teams. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 2) Management scientists use mathematical techniques to make decisions, which are then implemented by managers. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 3) Spreadsheets allow many managers to conduct their own analyses in management science studies. Answer: TRUE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 4) Managers must rely on management science experts to create and understand managerial problems. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application

5) Management science is a discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 6) The discovery of the simplex method in 1947 was the beginning of management science as a discipline. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 7) The rapid growth of computing capability and power has led to a corresponding rapid growth of the management science discipline. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 8) Managers make decisions based solely on the quantitative factors involved in the problem. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application

9) A management science team will try to conduct a systematic investigation of a problem that includes careful data gathering, developing and testing hypotheses, and then applying sound logic in the analysis. Answer: TRUE Difficulty: 3 Hard Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Apply AACSB: Reflective Thinking 10) The mathematical model of a business problem is the system of equations and related mathematical expressions that describes the essence of the problem. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 11) A mathematical model of a business problem allows a manager to evaluate both quantitative and qualitative aspects of the problem. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 12) Once management makes its decisions, the management science team typically is finished with its involvement in the problem. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application

13) A cost that varies with the production volume would be a fixed cost. Answer: FALSE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 14) A cost that varies with the production volume would be a variable cost. Answer: TRUE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 15) A cost that does not vary with the production volume would be a fixed cost. Answer: TRUE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 16) A cost that does not vary with the production volume would be a variable cost. Answer: FALSE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 17) At the break-even point, management is indifferent between producing a product and not producing it. Answer: TRUE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application

18) The best way to solve a break-even problem with a spreadsheet model is to try different production quantities until the quantity that leads to profits of zero is found. Answer: FALSE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a spreadsheet model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 19) A constraint is an algebraic variable that represents a quantifiable decision to be made. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 20) A decision variable is an algebraic variable that represents a quantifiable decision to be made. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 21) A parameter in a model is a variable that represents a decision to be made. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 22) The objective function for a model is a mathematical expression of the measure of performance for the problem in terms of the decision variables. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application

23) Sensitivity analysis is used to check the effect of changes in the model. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 24) Investigating the potential outcomes when estimates turn out to be incorrect is known as "what-if analysis." Answer: TRUE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 25) "What-if analysis" is a process used to generate estimates for use in mathematical models. Answer: FALSE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 26) Enlightened future managers should know which of the following? A) The power and relevance of management science. B) When management science can and cannot be applied. C) How to apply the major techniques of management science. D) How to interpret the results of a management science study. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application

27) The rapid development of the management science discipline can be credited in part to: A) World War I. B) George Dantzig. C) the computer revolution. D) George Dantzig and the computer revolution. E) World War I, George Dantzig, and the computer revolution. Answer: D Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Define the term management science Bloom's: Remember AACSB: Knowledge Application 28) Managers may base their decisions on which of the following? A) Quantitative factors. B) Their best judgment. C) Opinions from other managers. D) Past experience. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 29) Management science is based strongly on which of the following fields? A) Mathematics. B) Computer science. C) Business administration. D) Mathematics and computer science only. E) All of the answer choices are correct. Answer: D Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application

30) Which of the following are components of a mathematical model for decision making? A) Decision variables. B) An objective function. C) Constraints. D) Parameters. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 31) Which of the following are steps in a typical management science study? A) Define the problem and gather data. B) Formulate a model to represent the problem. C) Test the model and refine it as needed. D) Help to implement the recommendations. E) All of the answer choices are correct. Answer: E Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 32) Which of the following is a mathematical expression that gives the measure of performance for the problem? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. Answer: C Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application

33) Which of the following is a constant in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. Answer: B Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 34) Which of the following is an inequality or equation that expresses a restriction in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. Answer: D Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 35) A manager has determined that a potential new product can be sold at a price of $10.00 each. The cost to produce the product is $5.00, but the equipment necessary for production must be leased for $25,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. Answer: B Explanation: Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Apply AACSB: Knowledge Application 9 Copyright © 2019 McGraw-Hill

36) In order to produce a new product, a firm must lease equipment at a cost of $10,000 per year. The managers feel that they can sell 5,000 units per year at a price of $7.50. What is the highest variable cost that will allow the firm to at least break even on this project? A) $2.50. B) $3.50. C) $4.50. D) $5.50. E) $6.50. Answer: D Explanation:

, therefore

Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking 37) A manager has determined that a potential new product can be sold at a price of $20.00 each. The cost to produce the product is $10.00, but the equipment necessary for production must be leased for $75,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. Answer: C Explanation: Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application

38) Production has indicated that they can produce widgets at a cost of $4.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 4,000 units at $5.00 each. B) 3,000 units at $7.50 each. C) 1,500 units at $10.00 each. D) 1,000 units at $15.00 each E) 25,000 units. Answer: B Explanation: Calculating the break-even for each price, it is clear that 3,000 units at $7.50 each is the only option where the sales forecast exceeds the break-even point.

39) A manager has determined that a potential new product can be sold at a price of $50.00 each. The cost to produce the product is $35.00, but the equipment necessary for production must be leased for $100,000 per year. What is the break-even point? A) 3,333 units. B) 5,000 units. C) 6,667 units. D) 7,500 units. E) 8,167 units. Answer: C Explanation: Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Apply AACSB: Knowledge Application 40) In order to produce a new product, a firm must lease equipment at a cost of $25,000 per year. The managers feel that they can sell 10,000 units per year at a price of $15.00. What is the highest variable cost that will allow the firm to at least break even on this project? A) $12.50. B) $13.50. C) $14.50. D) $15.50. E) $16.50. Answer: A Explanation:

therefore

41) A manager has determined that a potential new product can be sold at a price of $100.00 each. The cost to produce the product is $75.00, but the equipment necessary for production must be leased for $175,000 per year. What is the break-even point? A) 3,000 units. B) 5,000 units. C) 7,000 units. D) 10,000 units. E) 25,000 units. Answer: C Explanation: Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Analytical Thinking

42) Production has indicated that they can produce widgets at a cost of $3.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 7,500 units at $17.50 each. B) 4,000 units at $20.00 each. C) 3,000 units at $22.50 each. D) 2,500 units at $25.00 each E) 1,500 units at $27.50 each. Answer: D Explanation: Calculating the break-even for each price, it is clear that 2,500 units at $25.00 each is the only option where the sales forecast equals the break-even point.

43) When evaluating a project to determine the break-even quantity, the advantage of a spreadsheet model is? A) Users can't see the formulas used. B) Calculations are always rounded to the nearest integer. C) The analyst can use Excel's "BREAKEVEN" function to perform the calculation D) A number of different estimates can be quickly evaluated once the model is constructed. E) There are no advantages to spreadsheet modeling of break-even analysis. Answer: D Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a spreadsheet model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 44) Which of the following is TRUE about the break-even point? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be negative. C) When sales are below the break-even point, profits will be positive. D) Once sales exceed the break-even point, profits no longer change if sales increase further. E) The total revenue and total cost are equal at the point where profits are maximized. Answer: A Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 45) Which of the following statements about the break-even quantity is FALSE? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be positive. C) When sales are below the break-even point, profits will be negative. D) Once sales exceed the break-even point, profits continue to increase as sales increase. E) The total revenue and total cost are equal at the point where profits are maximized. Answer: A Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application

46) Business analytics is a field which. A) is the same as operations research. B) aids managerial decision making through the use of data. C) uses descriptive analytics to predict the future. D) uses prescriptive analytics to analyze trends. E) uses predictive analytics to determine the best course of action. Answer: B Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application 47) Descriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. Answer: A Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application 48) Predictive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. Answer: B Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application

49) Prescriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. Answer: E Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application 50) In order to produce a new product, a firm must lease new equipment. The managers feel that they can sell 10,000 units per year at a price of $7.50. If the variable cost of production is $5.00 per unit, what is the most the firm can spend to lease the new equipment without losing money? A) $10,000. B) $15,000. C) $20,000. D) $25,000. E) $30,000. Answer: D Explanation:

therefore

If the firm has lease costs of $25,000 or less the product will not lose money. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking

, therefore

If the firm has rental costs of $750 or less the product will not lose money. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking

53) A tour company is planning a bus trip to a local museum. The company will lease a bus from a local bus owner for $400 and estimates that it will spend $15.00 per person for admission and lunch. Which of the following volume/price alternatives will allow the firm to avoid losing money on the trip? A) 20 customers at $30.00 each. B) 30 customers at $27.50 each. C) 40 customers at $25.00 each. D) 50 customers at $22.50 each E) 60 customers at $20.00 each. Answer: C Explanation: Calculating the break-even for each price, it is clear that 40 customers at $25.00 each is the only option where the sales forecast meets or exceeds the break-even point.

54) You have decided to start a vending machine business. A local store has space available for your machine but wants to charge you an annual fee to use the space. You estimate that you can sell 5,000 cans of soda each year. You sell a can of soda for $1.25, which allows you a profit of $0.50 per can. What is the most you would spend to lease the space for one year? A) $1,000. B) $2,500. C) $5,000. D) $7,500. E) $10,000. Answer: B Explanation: Since your price is $1.25 and your profit is $0.50, your cost per unit must be $1.25 – $0.50 = $0.75.

, therefore

If the store will lease the space for $2,500 or less the project will not lose money. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 2 Linear Programming: Basic Concepts 1) Linear programming problems may have multiple goals or objectives specified. 2) Linear programming allows a manager to find the best mix of activities to pursue and at what levels. 3) Linear programming problems always involve either maximizing or minimizing an objective function. 4) All linear programming models have an objective function and at least two constraints. 5) Constraints limit the alternatives available to a decision maker. 6) When formulating a linear programming problem on a spreadsheet, the data cells will show the optimal solution. 7) When formulating a linear programming problem on a spreadsheet, objective cells will show the levels of activities for the decisions being made. 8) When formulating a linear programming problem on a spreadsheet, the Excel equation for each output cell can typically be expressed as a SUMPRODUCT function. 9) One of the great strengths of spreadsheets is their flexibility for dealing with a wide variety of problems. 10) Linear programming problems can be formulated both algebraically and on spreadsheets. 11) The parameters of a model are the numbers in the data cells of a spreadsheet. 12) An example of a decision variable in a linear programming problem is profit maximization. 13) A feasible solution is one that satisfies all the constraints of a linear programming problem simultaneously. 14) An infeasible solution violates all of the constraints of the problem. 15) The best feasible solution is called the optimal solution. 16) Since all linear programming models must contain nonnegativity constraints, Solver will automatically include them and it is not necessary to add them to a formulation. 17) The line forming the boundary of what is permitted by a constraint is referred to as a parameter. 18) The origin satisfies any constraint with a ≥ sign and a positive right-hand side. 1 Copyright © 2019 McGraw-Hill

19) The feasible region only contains points that satisfy all constraints. 20) A circle would be an example of a feasible region for a linear programming problem. 21) The equation 5x + 7y = 10 is linear. 22) The equation 3xy = 9 is linear. 23) The graphical method can handle problems that involve any number of decision variables. 24) An objective function represents a family of parallel lines. 25) When solving linear programming problems graphically, there are an infinite number of possible objective function lines. 26) For a graph where the horizontal axis represents the variable x and the vertical axis represents the variable y, the slope of a line is the change in y when x is increased by 1. 27) The value of the objective function decreases as the objective function line is moved away from the origin. 28) A feasible point on the optimal objective function line is an optimal solution. 29) A linear programming problem can have multiple optimal solutions. 30) All constraints in a linear programming problem are either ≤ or ≥ inequalities. 31) Linear programming models can have either ≤ or ≥ inequality constraints but not both in the same problem. 32) A maximization problem can generally be characterized by having all ≥ constraints. 33) If a single optimal solution exists while using the graphical method to solve a linear programming problem, it will exist at a corner point. 34) When solving a maximization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible. 35) When solving a minimization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible. 36) A manager should know the following things about linear programming. A) What it is. B) When it should be used. C) When it should not be used. D) How to interpret the results of a study. E) All of the answer choices are correct. 2 Copyright © 2019 McGraw-Hill

37) Which of the following is not a component of a linear programming model? A) constraints B) decision variables C) parameters D) an objective E) a spreadsheet 38) In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as: A) optimal. B) feasible. C) nonnegative. D) targeted. E) All of the answer choices are correct. 39) When formulating a linear programming problem on a spreadsheet, which of the following is true? A) Parameters are called data cells. B) Decision variables are called changing cells. C) Nonnegativity constraints must be included. D) The objective function is called the objective cell. E) All of the answer choices are correct. 40)

Where are the data cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct.

41)

Where are the changing cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. 42)

Where is the objective cell located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct.

43)

Where are the output cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. 44) Which of the following could not be a constraint for a linear programming problem? A) 1A + 2B ≤ 3 B) 1A + 2B ≥ 3 C) 1A + 2B = 3 D) 1A + 2B E) 1A + 2B + 3C ≤ 3 45) For the products A, B, C, and D, which of the following could be a linear programming objective function? A) P = 1A + 2B +3C + 4D B) P = 1A + 2BC +3D C) P = 1A + 2AB +3ABC + 4ABCD D) P = 1A + 2B/C +3D E) All of the answer choices are correct. 46) After the data is collected the next step to formulating a linear programming model is to: A) identify the decision variables. B) identify the objective function. C) identify the constraints. D) specify the parameters of the problem. E) None of the answer choices are correct. 47) When using the graphical method, the region that satisfies all of the constraints of a linear programming problem is called the: A) optimum solution space. B) region of optimality. C) profit maximization space. D) feasible region. E) region of nonnegativity. 5 Copyright © 2019 McGraw-Hill

48) Solving linear programming problems graphically A) is possible with any number of decision variables. B) provides geometric intuition about what linear programming is trying to achieve. C) will always result in an optimal solution. D) All of the answers choices are correct. E) None of the answers choices are correct. 49) Which objective function has the same slope as this one: 4x + 2y = 20. A) 2x + 4y = 20 B) 2x − 4y = 20 C) 4x − 2y = 20 D) 8x + 8y = 20 E) 4x + 2y = 10 50) Given the following 2 constraints, which solution is a feasible solution for a maximization problem? (1) 14x1 + 6x2 ≤ 42 (2) x1 − x2 ≤ 3 A) (x1, x2) = (1, 5) B) (x1, x2) = (5, 1) C) (x1, x2) = (4, 4) D) (x1, x2) = (2, 1) E) (x1, x2) = (2, 6) 51) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 3x1 + 4x2 = 10 (2) 5x1 + 4x2 = 14 A) (x1, x2) = (2, 0.5) B) (x1, x2) = (4, 0.5) C) (x1, x2) = (2, 1) D) x1 = x2 E) x2 = 2x1

52) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 3x1 + 2x2 = 6 (2) 6x1 + 3x2 = 12 A) (x1, x2) = (1, 1.5) B) (x1, x2) = (0.5, 2) C) (x1, x2) = (0, 3) D) (x1, x2) = (2, 0) E) (x1, x2) = (0, 0) 53) What is the optimal solution for the following problem? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (2, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 0) D) (x, y) = (1, 5) E) None of the answer choices are correct. 54) Given the following 2 constraints, which solution is a feasible solution for a minimization problem? (1) 14x1 + 6x2 ≥ 42 (2) x1 + 3x2 ≥ 6 A) (x1, x2) = (0.5, 5). B) (x1, x2) = (0, 4). C) (x1, x2) = (2, 5). D) (x1, x2) = (1, 2). E) (x1, x2) = (2, 1). 55) Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 3x + 15y subject to 2x + 4y ≥ 12 5x + 2y ≥ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (0, 0). B) (x, y) = (0, 3). C) (x, y) = (0, 5). D) (x, y) = (1, 2.5). E) (x, y) = (6, 0). 7 Copyright © 2019 McGraw-Hill

56) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the objective function? A) P = A + 2B. B) P = 12A + 8B. C) P = 2A + B. D) P = 8A + 12B. E) P = 4A + 8B. 57) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Colombian beans? A) A + 2B ≤ 4,800. B) 12A + 8B ≤ 4,800. C) 2A + B ≤ 4,800. D) 8A + 12B ≤ 4,800. E) 4A + 8B ≤ 4,800. 58) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Dominican beans? A) 12A + 8B ≤ 4,800. B) 8A + 12B ≤ 4,800. C) 4A + 8B ≤ 3,200. D) 8A + 4B ≤ 3,200. E) 4A + 8B ≤ 4,800.

59) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. Which of the following is not a feasible solution? A) (A, B) = (0, 0). B) (A, B) = (0, 400). C) (A, B) = (200, 300). D) (A, B) = (400, 0). E) (A, B) = (400, 400). 60) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the weekly profit when producing the optimal amounts? A) $0. B) $400. C) $700. D) $800. E) $900. 61) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the objective function? A) P = 2L + 3D. B) P = 2L + 4D. C) P = 3L + 2D. D) P = 4L + 2D. E) P = 5L + 3D.

62) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the time constraint? A) 2L +3D ≤ 480. B) 2L + 4D ≤ 480. C) 3L + 2D ≤ 480. D) 4L + 2D ≤ 480. E) 5L + 3D ≤ 480. 63) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. Which of the following is not a feasible solution? A) (L, D) = (0, 0). B) (L, D) = (0, 120). C) (L, D) = (90, 75). D) (L, D) = (135, 0). E) (L, D) = (135, 120). 64) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the daily profit when producing the optimal amounts? A) $0. B) $240. C) $420. D) $405. E) $505.

65) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. What is the objective function? A) P = 4R + 6S B) P = 2R + 3S C) P = 6R + 4S D) P = 3R +2S E) P = 5R + 5S 66) What is the time constraint? A) 2R + 3S ≤ 720. B) 2R + 5S ≤ 720. C) 3R + 2S ≤ 720. D) 3R + 5S ≤ 720. E) 5R + 5S ≤ 720. 67) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. Which of the following is not a feasible solution? A) (R, S) = (0, 0) B) (R, S) = (0, 240) C) (R, S) = (180, 120) D) (R, S) = (300, 0) E) (R, S) = (180, 240) 68) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. What is the daily profit when producing the optimal amounts? A) $960 B) $1,560 C) $1,800 D) $1,900 E) $2,520 11 Copyright © 2019 McGraw-Hill

69) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the objective function? A) P = 4A + 1B B) P = 0.25A + 1B C) P = 1A + 4B D) P = 1A + 1B E) P = 0.25A + 0.5B 70) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the time constraint? A) 1A + 1B ≤ 800 B) 0.25A + 0.5B ≤ 800 C) 0.5A + 0.25B ≤ 800 D) 1A + 0.5B ≤ 800 E) 0.25A + 1B ≤ 800 71) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. Which of the following is not a feasible solution? A) (A, B) = (0, 0) B) (A, B) = (0, 1000) C) (A, B) = (1800, 700) D) (A, B) = (2500, 0) E) (A, B) = (100, 1600)

72) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the weekly profit when producing the optimal amounts? A) $10,000 B) $4,600 C) $2,500 D) $5,200 E) $6,400 73) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the objective function? A) P = 0.3B + 0.2C. B) P = 0.6B + 0.3C. C) P = 0.2B + 0.3C. D) P = 0.2B + 0.4C. E) P = 0.1B + 0.1C. 74) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the sugar constraint? A) 6B + 3C ≤ 4,800 B) 1B + 1C ≤ 4,800 C) 2B + 4C ≤ 4,800 D) 4B + 2C ≤ 4,800 E) 2B + 3C ≤ 4,800

75) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. Which of the following is not a feasible solution? A) (B, C) = (0, 0) B) (B, C) = (0, 1100) C) (B, C) = (800, 600) D) (B, C) = (1100, 0) E) (B, C) = (0, 1400) 76) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the daily profit when producing the optimal amounts? A) $580 B) $340 C) $220 D) $380 E) $420 77) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the objective function? A) P = 0.5D + 0.4C B) P = 0.2D + 0.3C C) P = 0.4D + 0.5C D) P = 0.1D + 0.2C E) P = 0.6D + 0.8C

78) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the sugar constraint? A) 2D + 3C ≤ 4,800 B) 6D + 8C ≤ 4,800 C) 1D + 2C ≤ 4,800 D) 3D + 2C ≤ 4,800 E) 4D + 5C ≤ 4,800 79) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. Which of the following is not a feasible solution? A) (D, C) = (0, 0) B) (D, C) = (0, 1000) C) (D, C) = (800, 600) D) (D, C) = (1600, 0) E) (D, C) = (0, 1,200) 80) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the daily profit when producing the optimal amounts? A) $800 B) $500 C) $640 D) $620 E) $600

81) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the objective function? A) P = 150D + 300T B) P = 500D + 300T C) P = 300D + 500T D) P = 300D + 150T E) P = 100D + 90T 82) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the storage space constraint? A) 90D + 100T ≤ 18,000 B) 100D + 90T ≥ 18,000 C) 300D + 90T ≤ 18,000 D) 500D + 100T ≤ 18,000 E) 100D + 90T ≤ 18,000 83) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. Which of the following is not a feasible solution? A) (D, T) = (0, 0) B) (D, T) = (0, 250) C) (D, T) = (150, 0) D) (D, T) = (90, 100) E) (D, T) = (0, 200)

84) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the weekly profit when ordering the optimal amounts? A) $0 B) $30,000 C) $42,000 D) $45,000 E) $54,000 85) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 4x1 + 2x2 = 7 (2) 4x1 - 3x2 = 2 A) (x1, x2) = (1, 1.25) B) (x1, x2) = (1.25, 1) C) (x1, x2) = (0, 3) D) (x1, x2) = (1.25, 0) E) (x1, x2) = (0, 0) 86) Use the graphical method for linear programming to find the optimal solution for the following problem. Maximize P = 4x + 5 y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (2, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 0) D) (x, y) = (1, 5) E) None of the answer choices are correct.

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 2 Linear Programming: Basic Concepts 1) Linear programming problems may have multiple goals or objectives specified. Answer: FALSE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) Linear programming allows a manager to find the best mix of activities to pursue and at what levels. Answer: TRUE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) Linear programming problems always involve either maximizing or minimizing an objective function. Answer: TRUE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) All linear programming models have an objective function and at least two constraints. Answer: FALSE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

5) Constraints limit the alternatives available to a decision maker. Answer: TRUE Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) When formulating a linear programming problem on a spreadsheet, the data cells will show the optimal solution. Answer: FALSE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) When formulating a linear programming problem on a spreadsheet, objective cells will show the levels of activities for the decisions being made. Answer: FALSE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) When formulating a linear programming problem on a spreadsheet, the Excel equation for each output cell can typically be expressed as a SUMPRODUCT function. Answer: TRUE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

9) One of the great strengths of spreadsheets is their flexibility for dealing with a wide variety of problems. Answer: TRUE Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 10) Linear programming problems can be formulated both algebraically and on spreadsheets. Answer: TRUE Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) The parameters of a model are the numbers in the data cells of a spreadsheet. Answer: TRUE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Name and identify the purpose of the four kinds of cells used in linear programming spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) An example of a decision variable in a linear programming problem is profit maximization. Answer: FALSE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Name and identify the purpose of the four kinds of cells used in linear programming spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) A feasible solution is one that satisfies all the constraints of a linear programming problem simultaneously. Answer: TRUE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) An infeasible solution violates all of the constraints of the problem. Answer: FALSE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) The best feasible solution is called the optimal solution. Answer: TRUE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Explain what linear programming is. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) Since all linear programming models must contain nonnegativity constraints, Solver will automatically include them and it is not necessary to add them to a formulation. Answer: FALSE Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

17) The line forming the boundary of what is permitted by a constraint is referred to as a parameter. Answer: FALSE Difficulty: 1 Easy Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) The origin satisfies any constraint with a ≥ sign and a positive right-hand side. Answer: FALSE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) The feasible region only contains points that satisfy all constraints. Answer: TRUE Difficulty: 1 Easy Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) A circle would be an example of a feasible region for a linear programming problem. Answer: FALSE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

21) The equation 5x + 7y = 10 is linear. Answer: TRUE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Present the algebraic form of a linear programming model from its formulation on a spreadsheet. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) The equation 3xy = 9 is linear. Answer: FALSE Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Present the algebraic form of a linear programming model from its formulation on a spreadsheet. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) The graphical method can handle problems that involve any number of decision variables. Answer: FALSE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 24) An objective function represents a family of parallel lines. Answer: TRUE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

25) When solving linear programming problems graphically, there are an infinite number of possible objective function lines. Answer: TRUE Difficulty: 1 Easy Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) For a graph where the horizontal axis represents the variable x and the vertical axis represents the variable y, the slope of a line is the change in y when x is increased by 1. Answer: TRUE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 27) The value of the objective function decreases as the objective function line is moved away from the origin. Answer: FALSE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 28) A feasible point on the optimal objective function line is an optimal solution. Answer: TRUE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 7 Copyright © 2019 McGraw-Hill

29) A linear programming problem can have multiple optimal solutions. Answer: TRUE Difficulty: 1 Easy Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) All constraints in a linear programming problem are either ≤ or ≥ inequalities. Answer: FALSE Difficulty: 1 Easy Topic: Using excel's solver to solve linear programming problems Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) Linear programming models can have either ≤ or ≥ inequality constraints but not both in the same problem. Answer: FALSE Difficulty: 1 Easy Topic: Using excel's solver to solve linear programming problems Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 32) A maximization problem can generally be characterized by having all ≥ constraints. Answer: FALSE Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

33) If a single optimal solution exists while using the graphical method to solve a linear programming problem, it will exist at a corner point. Answer: TRUE Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 34) When solving a maximization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible. Answer: TRUE Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 35) When solving a minimization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible. Answer: FALSE Explanation: Multiple-Choice Questions Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

36) A manager should know the following things about linear programming. A) What it is. B) When it should be used. C) When it should not be used. D) How to interpret the results of a study. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: Formulating the Wyndor problem on a spreadsheet Learning Objective: Identify the three key questions to be addressed in formulating any spreadsheet model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 37) Which of the following is not a component of a linear programming model? A) constraints B) decision variables C) parameters D) an objective E) a spreadsheet Answer: E Difficulty: 1 Easy Topic: Formulating the Wyndor problem on a spreadsheet Learning Objective: Name and identify the purpose of the four kinds of cells used in linear programming spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as: A) optimal. B) feasible. C) nonnegative. D) targeted. E) All of the answer choices are correct. Answer: B Difficulty: 1 Easy Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10 Copyright © 2019 McGraw-Hill

39) When formulating a linear programming problem on a spreadsheet, which of the following is true? A) Parameters are called data cells. B) Decision variables are called changing cells. C) Nonnegativity constraints must be included. D) The objective function is called the objective cell. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 40)

Where are the data cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. Answer: B Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

41)

Where are the changing cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. Answer: C Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

42)

Where is the objective cell located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. Answer: D Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

43)

Where are the output cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. Answer: E Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 44) Which of the following could not be a constraint for a linear programming problem? A) 1A + 2B ≤ 3 B) 1A + 2B ≥ 3 C) 1A + 2B = 3 D) 1A + 2B E) 1A + 2B + 3C ≤ 3 Answer: D Explanation: A constraint requires both a left-hand side (level of activities) and right-hand side (feasible value). Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Name and identify the purpose of the four kinds of cells used in linear programming spreadsheet models. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

45) For the products A, B, C, and D, which of the following could be a linear programming objective function? A) P = 1A + 2B +3C + 4D B) P = 1A + 2BC +3D C) P = 1A + 2AB +3ABC + 4ABCD D) P = 1A + 2B/C +3D E) All of the answer choices are correct. Answer: A Explanation: A linear objective function can only include products of a changing cell and a data cell. Only option "a" can be represented with a SUMPRODUCT function in Excel. Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Name and identify the purpose of the four kinds of cells used in linear programming spreadsheet models. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 46) After the data is collected the next step to formulating a linear programming model is to: A) identify the decision variables. B) identify the objective function. C) identify the constraints. D) specify the parameters of the problem. E) None of the answer choices are correct. Answer: A Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

47) When using the graphical method, the region that satisfies all of the constraints of a linear programming problem is called the: A) optimum solution space. B) region of optimality. C) profit maximization space. D) feasible region. E) region of nonnegativity. Answer: D Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 48) Solving linear programming problems graphically A) is possible with any number of decision variables. B) provides geometric intuition about what linear programming is trying to achieve. C) will always result in an optimal solution. D) All of the answers choices are correct. E) None of the answers choices are correct. Answer: B Difficulty: 2 Medium Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

49) Which objective function has the same slope as this one: 4x + 2y = 20. A) 2x + 4y = 20 B) 2x − 4y = 20 C) 4x − 2y = 20 D) 8x + 8y = 20 E) 4x + 2y = 10 Answer: E Explanation: To determine the slope of the objective function, solve for the variable "y." y = −2x + 10 indicates a slope of −2. Only option "e" has the same slope. Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 50) Given the following 2 constraints, which solution is a feasible solution for a maximization problem? (1) 14x1 + 6x2 ≤ 42 (2) x1 − x2 ≤ 3 A) (x1, x2) = (1, 5) B) (x1, x2) = (5, 1) C) (x1, x2) = (4, 4) D) (x1, x2) = (2, 1) E) (x1, x2) = (2, 6) Answer: D Explanation: To determine feasibility, substitute the variable values into the constraints. Substituting option "d" values of x1 and x2 leaves both constraints satisfied. (1) 14x1 + 6x2 ≤ 42 ⇒ 14(2) + 6(1) = 34 ≤ 42 (2) x1x2 ≤ 3⇒ 1(2) - 1(1) = 3 ≤ 3 Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

51) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 3x1 + 4x2 = 10 (2) 5x1 + 4x2 = 14 A) (x1, x2) = (2, 0.5) B) (x1, x2) = (4, 0.5) C) (x1, x2) = (2, 1) D) x1 = x2 E) x2 = 2x1 Answer: C Explanation: Using subtraction to eliminate one variable (x2) allows solving for the other (x1). Then substitution of the value for x1 into an original equation allows us to solve for x2. 3x1 + 4x2 = 10 −(5x1 + 4x2 = 14) −2x1 + 0x2 = −4 ⇒ x1 = 2 Since x = 2, 3x1 + 4x2 = 10 ⇒ 4x2 = 4 ⇒ x2 = 1 Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

52) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 3x1 + 2x2 = 6 (2) 6x1 + 3x2 = 12 A) (x1, x2) = (1, 1.5) B) (x1, x2) = (0.5, 2) C) (x1, x2) = (0, 3) D) (x1, x2) = (2, 0) E) (x1, x2) = (0, 0) Answer: D Explanation: Using subtraction to eliminate one variable (x1) allows solving for the other (x2). Then substitution of the value for x2 into an original equation allows us to solve for x1. 2(3x1 + 2x2 = 6) {this equation is multiplied by 2 to allow elimination of x1) -(6x1 + 3x2 = 12) 0x1 - 2x2 = 0 ⇒ x2 = 0 Since x2 = 0, 3x1 + 2x2 = 6 ⇒ 3x1 = 6 ⇒ x1= 2 Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

53) What is the optimal solution for the following problem? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (2, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 0) D) (x, y) = (1, 5) E) None of the answer choices are correct. Answer: B Explanation: Graph the two constraints to define the feasible region. Next, find the objective function value that just touches the edge of the feasible region (here, at point (0, 3) the objective function is maximized with a value of 45. Alternatively, evaluate the extreme points of the feasible region: (0, 0) - objective function value 0 (1.2, 0) - objective function value 3.6 (0, 3) - objective function value 45 {maximum}

Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

54) Given the following 2 constraints, which solution is a feasible solution for a minimization problem? (1) 14x1 + 6x2 ≥ 42 (2) x1 + 3x2 ≥ 6 A) (x1, x2) = (0.5, 5). B) (x1, x2) = (0, 4). C) (x1, x2) = (2, 5). D) (x1, x2) = (1, 2). E) (x1, x2) = (2, 1). Answer: C Explanation: To determine feasibility, substitute the variable values into the constraints. Substituting option "c" values of x1 and x2 leaves both constraints satisfied. (1) 14x1 + 6x2 ≥ 42 ⇒ 14(2) + 6(5) = 48 ≥ 42 (2) x1 + 3x2 ≥ 6 ⇒ 1(2) + 3(5) = 17 ≥ 6 Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

55) Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 3x + 15y subject to 2x + 4y ≥ 12 5x + 2y ≥ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (0, 0). B) (x, y) = (0, 3). C) (x, y) = (0, 5). D) (x, y) = (1, 2.5). E) (x, y) = (6, 0). Answer: E Explanation: Graph the two constraints to define the feasible region. Next, find the objective function value that just touches the edge of the feasible region (here, at point (6, 0) the objective function is minimized with a value of 18. Alternatively, evaluate the extreme points of the feasible region: (6, 0) - objective function value 18 {minimum} (0, 5) - objective function value 75 (1, 2.5) - objective function value 40.5

Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 22 Copyright © 2019 McGraw-Hill

57) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Colombian beans? A) A + 2B ≤ 4,800. B) 12A + 8B ≤ 4,800. C) 2A + B ≤ 4,800. D) 8A + 12B ≤ 4,800. E) 4A + 8B ≤ 4,800. Answer: B Explanation: Since each pound of A uses 12 ounces of Colombian beans and each pound of B uses 8 ounces of Colombian beans, it is convenient to convert the supply of Columbian beans to ounces (300 pounds = 4,800 ounces). Then the constraint should reflect that the usages (12 ounces per pound of A, 8 ounces per pound of B) must be less than the supply. Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

58) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Dominican beans? A) 12A + 8B ≤ 4,800. B) 8A + 12B ≤ 4,800. C) 4A + 8B ≤ 3,200. D) 8A + 4B ≤ 3,200. E) 4A + 8B ≤ 4,800. Answer: C Explanation: Since each pound of A uses 12 ounces of Dominican beans and each pound of B uses 8 ounces of Dominican beans, it is convenient to convert the supply of Dominican beans to ounces (200 pounds = 3,200 ounces). Then the constraint should reflect that the usages (4 ounces per pound of A, 8 ounces per pound of B) must be less than the supply. Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

60) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the weekly profit when producing the optimal amounts? A) $0. B) $400. C) $700. D) $800. E) $900. Answer: D Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown below is A = 400, B = 0, with weekly profits of $800. Maximize P = 2A + B subject to 12A + 4B ≤ 4,800 4A + 8B ≤ 3,600 and A ≥ 0, B ≥ 0. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

61) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the objective function? A) P = 2L + 3D. B) P = 2L + 4D. C) P = 3L + 2D. D) P = 4L + 2D. E) P = 5L + 3D. Answer: C Explanation: Since the objective is to maximize profits, the objective function should reflect the profitability of L ($3.00 per keg) and D ($2.00 per keg). Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

63) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. Which of the following is not a feasible solution? A) (L, D) = (0, 0). B) (L, D) = (0, 120). C) (L, D) = (90, 75). D) (L, D) = (135, 0). E) (L, D) = (135, 120). Answer: E Explanation: To determine feasibility, substitute the variable values into the constraints. Substituting option "e" values of L and D violates both constraints. (1) 2L + 4D ≤ 480 ⇒ 2(135) + 4(120) = 750 ≥ 480 (2) 5L + 3D ≤ 675 ⇒ 5(135) + 3(120) = 1,035 ≥ 675 Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

64) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the daily profit when producing the optimal amounts? A) $0. B) $240. C) $420. D) $405. E) $505. Answer: C Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown below is L = 90, D = 75, with weekly profits of $420. Maximize P = 3L + 2D subject to 2L + 3D ≤ 480 5L + 2D ≤ 675 and L ≥ 0, D ≥ 0. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

65) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. What is the objective function? A) P = 4R + 6S B) P = 2R + 3S C) P = 6R + 4S D) P = 3R +2S E) P = 5R + 5S Answer: C Explanation: Since the objective is to maximize profits, the objective function should reflect the profitability of R ($6.00 per case) and S ($4.00 per case). Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 66) What is the time constraint? A) 2R + 3S ≤ 720. B) 2R + 5S ≤ 720. C) 3R + 2S ≤ 720. D) 3R + 5S ≤ 720. E) 5R + 5S ≤ 720. Answer: A Explanation: Since each case of R requires 2 minutes and each case of S uses 3 minutes, it is convenient to convert the available time to minutes (12 hours = 720 minutes). Then the constraint should reflect that the usages (2 minutes for R, 3 minutes for S) must be less than the supply. Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

67) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. Which of the following is not a feasible solution? A) (R, S) = (0, 0) B) (R, S) = (0, 240) C) (R, S) = (180, 120) D) (R, S) = (300, 0) E) (R, S) = (180, 240) Answer: E Explanation: To determine feasibility, substitute the variable values into the constraints. Substituting option "e" values of R and S violates both constraints. (1) 2R + 3S ≤ 720 ⇒ 2(180) + 3(240) = 1,080 ≥ 720 (2) 5R + 5S ≤ 1,500 ⇒ 5(180) + 5(240) = 2,100 ≥ 1,500 Difficulty: 1 Easy Topic: The Mathematical Model in the Spreadsheet Learning Objective: Present the algebraic form of a linear programming model from its formulation on a spreadsheet. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

68) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. What is the daily profit when producing the optimal amounts? A) $960 B) $1,560 C) $1,800 D) $1,900 E) $2,520 Answer: C Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown below is R = 300, S = 0, with weekly profits of $1,800. Maximize P = 6R + 4S subject to 6R + 4S ≤ 720 5R + 5S ≤ 1,500 and R ≥ 0, S ≥ 0. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation

70) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the time constraint? A) 1A + 1B ≤ 800 B) 0.25A + 0.5B ≤ 800 C) 0.5A + 0.25B ≤ 800 D) 1A + 0.5B ≤ 800 E) 0.25A + 1B ≤ 800 Answer: B Explanation: Since each A requires 15 minutes and each B uses 30 minutes, it is convenient to convert the required time to hours. Then the constraint should reflect that the usages (0.25 hour for A, 0.5 hour for B) must be less than the supply. Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

71) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. Which of the following is not a feasible solution? A) (A, B) = (0, 0) B) (A, B) = (0, 1000) C) (A, B) = (1800, 700) D) (A, B) = (2500, 0) E) (A, B) = (100, 1600) Answer: E Explanation: To determine feasibility, substitute the variable values into the constraints. Substituting option "e" values of A and B violates at least one constraint. (1) 0.25A + 0.5B ≤ 800 ⇒ 2(100) + 3(1,600) = 5,000 ≥ 800 {constraint violated} (2) A + B ≤ 2,500 ⇒ 100 + 1,600 = 1,700 ≤ 2500 (3) A ≤ 4,000 ⇒ 100 ≥ 4,000 (4) B ≤ 1,000 ⇒ 1,600 ≥ 1,000 {constraint violated} Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

73) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the objective function? A) P = 0.3B + 0.2C. B) P = 0.6B + 0.3C. C) P = 0.2B + 0.3C. D) P = 0.2B + 0.4C. E) P = 0.1B + 0.1C. Answer: C Explanation: Since the objective is to maximize profits, the objective function should reflect the profitability of B ($0.20 per unit) and C ($0.30 per unit). Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 74) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the sugar constraint? A) 6B + 3C ≤ 4,800 B) 1B + 1C ≤ 4,800 C) 2B + 4C ≤ 4,800 D) 4B + 2C ≤ 4,800 E) 2B + 3C ≤ 4,800 Answer: C Explanation: Since each B requires 2 tablespoons of sugar and each C requires 4 tablespoons of sugar, the constraint should reflect that the usages (2 tablespoons for each B, 4 tablespoons for each C) must be less than the supply. Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 39 Copyright © 2019 McGraw-Hill

76) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the daily profit when producing the optimal amounts? A) $580 B) $340 C) $220 D) $380 E) $420 Answer: D Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown below is B = 1,200, C = 1,000, with weekly profits of $5,200. Maximize P = 0.2B + 0.3C subject to 2B + 4C ≤ 4,800 6B + 3C ≤ 6,600 B + C ≤ 1,400 and B ≥ 0, C ≥ 0. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation

77) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the objective function? A) P = 0.5D + 0.4C B) P = 0.2D + 0.3C C) P = 0.4D + 0.5C D) P = 0.1D + 0.2C E) P = 0.6D + 0.8C Answer: C Explanation: Since the objective is to maximize profits, the objective function should reflect the profitability of D($0.40 per box) and C ($0.50 per box). Difficulty: 2 Medium Topic: Using excel's solver to solve linear programming problems Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

79) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. Which of the following is not a feasible solution? A) (D, C) = (0, 0) B) (D, C) = (0, 1000) C) (D, C) = (800, 600) D) (D, C) = (1600, 0) E) (D, C) = (0, 1,200) Answer: E Explanation: To determine feasibility, substitute the variable values into the constraints. Substituting option "e" values of D and C violates at least one constraint. (1) 2D + 3C ≤ 4,800 ⇒ 2(0) + 3(1,200) = 3,600 ≤ 4,800 (2) 6D + 8C ≤ 9,600 ⇒ 6(0) + 8(1,200) = 9,600 = 9,600 (3) D + 2C ≤ 2,000 ⇒ 1(0) + 2(1,200) = 2,400 ≥ 1,400 {constraint violated} Difficulty: 2 Medium Topic: Using excel's solver to solve linear programming problems Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

80) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the daily profit when producing the optimal amounts? A) $800 B) $500 C) $640 D) $620 E) $600 Answer: C Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown below is D = 1,600, C = 0, with weekly profits of $640. Maximize P = 0.4D + 0.5C subject to 2D + 3C ≤ 4,800 6D + 8C ≤ 9,600 D + 2C ≤ 2,000 and D ≥ 0, C ≥ 0. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation

81) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the objective function? A) P = 150D + 300T B) P = 500D + 300T C) P = 300D + 500T D) P = 300D + 150T E) P = 100D + 90T Answer: D Explanation: Since the objective is to maximize profits, the objective function should reflect the profitability of D($300 per bed) and T ($150 per bed). Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 82) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the storage space constraint? A) 90D + 100T ≤ 18,000 B) 100D + 90T ≥ 18,000 C) 300D + 90T ≤ 18,000 D) 500D + 100T ≤ 18,000 E) 100D + 90T ≤ 18,000 Answer: E Explanation: Since each D requires 100 cubic feet and each T requires 90 cubic feet, the constraint should reflect that the usages (100 cubic feet for each D, 90 cubic feet for each C) must be less than the supply. Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 46 Copyright © 2019 McGraw-Hill

83) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. Which of the following is not a feasible solution? A) (D, T) = (0, 0) B) (D, T) = (0, 250) C) (D, T) = (150, 0) D) (D, T) = (90, 100) E) (D, T) = (0, 200) Answer: B Explanation: To determine feasibility, substitute the variable values into the constraints. Substituting option "b" values of D and T violates at least one constraint. (1) 100D + 90T ≤ 18,000 ⇒ 100(0) + 90(250) = 22,500 ≥18,000 {constraint violated} (2) 500D + 300C ≤ 75,000 ⇒ 500(0) + 300(250) = 75,000 = 75,000 Difficulty: 2 Medium Topic: The Mathematical Model in the Spreadsheet Learning Objective: Formulate a basic linear programming model in a spreadsheet from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

84) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the weekly profit when ordering the optimal amounts? A) $0 B) $30,000 C) $42,000 D) $45,000 E) $54,000 Answer: D Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown below is D = 150, T = 0, with weekly profits of $45,000. Maximize P = 300D + 150T subject to 100D + 90T ≤ 18,000 300D + 150T ≤ 75,000 and D ≥ 0, T ≥ 0. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation

85) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 4x1 + 2x2 = 7 (2) 4x1 - 3x2 = 2 A) (x1, x2) = (1, 1.25) B) (x1, x2) = (1.25, 1) C) (x1, x2) = (0, 3) D) (x1, x2) = (1.25, 0) E) (x1, x2) = (0, 0) Answer: B Explanation: Using subtraction to eliminate one variable (x1) allows solving for the other (x2). Then substitution of the value for x2 into an original equation allows us to solve for x1. 4x1 + 2x2 = 7 − (4x1 − 3x2 = 2) 0x1 + 5x2 = 5 ⇒ x2 = 1 Since x2 = 1, 4x1 + 2x2 = 7 ⇒ 4x1 = 5 ⇒ x1 = 1.25 Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

86) Use the graphical method for linear programming to find the optimal solution for the following problem. Maximize P = 4x + 5 y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (2, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 0) D) (x, y) = (1, 5) E) None of the answer choices are correct. Answer: B Explanation: Graph the two constraints to define the feasible region. Next, find the objective function value that just touches the edge of the feasible region (here, at point (2/3, 4 2/3) the objective function is maximized with a value of 26. Alternatively, evaluate the extreme points of the feasible region: (0, 0) - objective function value 0 (3, 0) - objective function value 12 (0, 5) - objective function value 25 (2/3, 4 2/3) - objective function value 26 {maximum}

87) Using Excel's Solver add-in, find the optimal solution for the following problem? Maximize P = 3x + 8y subject to 2x + 4y ≤ 20 6x + 3y ≤ 18 and x ≥ 0, y ≥ 0. A) (x, y) = (2, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 0) D) (x, y) = (0, 5) E) None of the answer choices are correct. Answer: D Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown above is x = 0, y = 5, with an objective function value of 40. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation 88) Using Excel's Solver add-in, find the optimal solution for the following problem? Maximize P = 8x + 3y subject to 2x + 4y ≤ 20 6x + 3y ≤ 18 and x ≥ 0, y ≥ 0. A) (x, y) = (3, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 0) D) (x, y) = (0, 5) E) None of the answer choices are correct. Answer: A Explanation: Using Excel's Solver add-in, the optimal solution of the linear program shown above is x = 3, y = 0, with an objective function value of 24. Difficulty: 3 Hard Topic: Using excel's solver to solve linear programming problems Learning Objective: Use Excel to solve a linear programming spreadsheet model. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation

89) Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 6x + 10y subject to 2x + 4y ≥ 12 5x + 2y ≥ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (0, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 5) D) (x, y) = (1, 2.5) E) (x, y) = (6, 0) Answer: D Explanation: Graph the two constraints to define the feasible region. Next, find the objective function value that just touches the edge of the feasible region (here, at point (1, 2.5) the objective function is minimized with a value of 31. Alternatively, evaluate the extreme points of the feasible region: (6, 0) - objective function value 36 (0, 5) - objective function value 50 (1, 2.5) - objective function value 31 {minimum}

Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 52 Copyright © 2019 McGraw-Hill

90) Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 12x + 4y subject to 2x + 4y ≥ 12 5x + 2y ≥ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (0, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 5) D) (x, y) = (1, 2.5) E) (x, y) = (6, 0) Answer: C Explanation: Graph the two constraints to define the feasible region. Next, find the objective function value that just touches the edge of the feasible region (here, at point (0, 5) the objective function is minimized with a value of 20). Alternatively, evaluate the extreme points of the feasible region: (6, 0) - objective function value 72 (0, 5) - objective function value 20 {minimum} (1, 2.5) - objective function value 22

Difficulty: 3 Hard Topic: The graphical method for solving two-variable problems Learning Objective: Apply the graphical method to solve a two-variable linear programming problem. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 53 Copyright © 2019 McGraw-Hill

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 3 Linear Programming: Formulation and Applications 1) When formulating a linear programming model on a spreadsheet, the decisions to be made are located in the data cells. 2) When formulating a linear programming model on a spreadsheet, the constraints are located (in part) in the output cells. 3) When formulating a linear programming model on a spreadsheet, the measure of performance is located in the objective cell. 4) A mathematical model will be an exact representation of the real problem. 5) Approximations and simplifying assumptions generally are required to have a workable model. 6) Linear programming does not permit fractional solutions. 7) When formulating a linear programming problem on a spreadsheet, data cells will show the levels of activities for the decisions being made. 8) A key assumption of linear programming is that the equation for each of the output cells, including the objective cell, can be expressed as a SUMPRODUCT (or SUM) function. 9) Resource-allocation problems are linear programming problems involving the allocation of limited resources to activities. 10) Strict inequalities (i.e., < or >) are not permitted in linear programming formulations. 11) When studying a resource-allocation problem, it is necessary to determine the contribution per unit of each activity to the overall measure of performance. 12) It is usually quite simple to obtain estimates of parameters in a linear programming problem. 13) The objective cell is a special kind of output cell. 14) Financial planning is one of the most important areas of application for cost-benefit-tradeoff problems. 15) A resource constraint refers to any functional constraint with a ≥ sign in a linear programming model. 16) In the algebraic form of a resource constraint, the coefficient of each decision variable is the resource usage per unit of the corresponding activity. 17) Cost-benefit-tradeoff problems are linear programming problems involving the allocation of limited resources to activities. 1 Copyright © 2019 McGraw-Hill

18) For cost-benefit-tradeoff problems, minimum acceptable levels for each kind of benefit are prescribed and the objective is to achieve all these benefits with minimum cost. 19) A benefit constraint refers to a functional constraint with a ≥ sign in a linear programming model. 20) In most cases, the minimum acceptable level for a cost-benefit-tradeoff problem is set by how much money is available. 21) It is the nature of the application that determines the classification of the resulting linear programming formulation. 22) It is the nature of the restrictions imposed on the decisions regarding the mix of activity levels that determines the classification of the resulting linear programming formulation. 23) It is fairly common to have both resource constraints and benefit constraints in the same formulation. 24) Choosing the best tradeoff between cost and benefits is a managerial judgment decision. 25) Having one requirement for each location is a characteristic common to all transportation problems. 26) Fixed-requirement constraints in a linear programming model are functional constraints that use an equal sign. 27) The capacity row in a distribution-network formulation shows the maximum number of units than can be shipped through the network. 28) Once a linear programming problem has been formulated, it is rare to make major adjustments to it. 29) A mixed linear programming problem will always contain some of each of the three types of constraints in it. 30) Blending problems are a special type of mixed linear programming problems. 31) Model formulation should precede problem formulation. 32) When dealing with huge real problems, there is no such thing as the perfectly correct linear programming model for the problem. 33) Transportation problems are concerned with distributing commodities from sources to destinations in such a way as to minimize the total distribution cost. 34) Transportation problems always involve shipping goods from one location to another.

35) The requirements assumption states that each source has a fixed supply of units, where the entire supply must be distributed to the destinations and that each destination has a fixed demand for units, where the entire demand must be received from the sources. 36) A transportation problem requires a unit cost for every source-destination combination. 37) An assignment problem is a special type of transportation problem. 38) Generally, assignment problems match people to an equal number of tasks at a minimum cost. 39) A transportation problem will always return integer values for all decision variables. 40) In an assignment problem, it is necessary to add an integer constraint to the decision variables to ensure that they will take on a value of either 0 or 1. 41) A linear programming problem may return fractional solutions (e.g. 4 1/3) for a resource allocation problem. 42) In a cost-benefit-trade-off problem, management defines the maximum amount that can be spent and the objective is to maximize benefits within this cost target. 43) Transportation and assignment problems are examples of fixed-requirement problems. 44) A transportation problem with 3 factories and 4 customers will have 12 shipping lanes. 45) A transportation problem with 3 factories and 4 customers will have 12 fixed-requirement constraints. 46) Which of the following are categories of linear programming problems? A) Resource-allocation problems. B) Cost-benefit-tradeoff problems. C) Distribution-network problems. D) All of the above. E) None of the above. 47) A linear programming model contains which of the following components? A) Data. B) Decisions. C) Constraints. D) Measure of performance. E) All of the answer choices are correct. 48) In linear programming formulations, it is possible to have the following types of constraints: A) ≤. B) >. C) =. D) ≤ and > only. E) All of the answer choices are correct. 3 Copyright © 2019 McGraw-Hill

49) Resource-allocation problems have the following type of constraints: A) ≥. B) ≤. C) =. D) <. E) None of the answer choices are correct. 50) When formulating a linear programming problem on a spreadsheet, which of the following is true? A) Parameters are called data cells. B) Decision variables are called changing cells. C) Right hand sides are part of the constraints. D) The objective function is called the objective cell. E) All of the answer choices are correct. 51)

Where are data cells located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10

52)

Where are the changing cells located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10 53)

Where is the objective cell located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10

54)

Where are the output cells located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10 55) Cost-benefit tradeoff problems have the following type of constraints: A) ≥ B) ≤ C) = D) < E) None of the answer choices are correct. 56) Mixed problems may have the following type of constraints: A) ≥. B) ≤. C) =. D) All of the answer choices are correct. E) None of the answer choices are correct. 57) A linear programming problem where the objective is to find the best mix of ingredients for a product to meet certain specifications is called: A) a resource-allocation problem. B) a blending problem. C) a cost-benefit tradeoff problem. D) a mixture problem. E) None of the answer choices are correct. 58) Using techniques to test the initial versions of a model to identify errors and omissions is called: A) model validation. B) model enrichment. C) model enhancement. D) model debugging. E) None of the answer choices are correct.

59) Starting with a simple version of a model and adding to it until it reflects the real problem is called: A) model validation. B) model enrichment. C) model enhancement. D) model elaboration. E) None of the answer choices are correct. 60) The transportation model method for evaluating location alternatives minimizes: A) the number of sources. B) the number of destinations. C) total supply. D) total demand. E) total shipping cost. 61) Which of the following is not information needed to use the transportation model? A) Capacity of the sources. B) Demand of the destinations. C) Unit shipping costs. D) Unit shipping distances. E) All of the answer choices are correct. 62) When formulating a transportation problem on a spreadsheet, which of the following are necessary? A) A table of data. B) A network representation. C) A table for the solution. D) A table of data and a table for the solution only. E) All of the answer choices are correct. 63) An assignment problem: A) is a special transportation problem. B) will always have an integer solution. C) has all supplies and demands equal to 1. D) None of the answer choices are correct. E) All of the answer choices are correct. 64) Applications of assignment problems may include: A) matching personnel to jobs. B) assigning machines to tasks. C) designing bussing routes. D) matching personnel to jobs and assigning machines to tasks only. E) matching personnel to jobs, assigning machines to tasks, and designing bussing routes.

65) A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). The writer's problem falls within which classification? A) Resource-allocation. B) Cost-benefit-trade-off. C) Mixed problems. D) Transportation problems. E) Assignment problems. 66) A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). Which of the following is the objective function for the writer's problem? A) Max R = 45N + 400M − 20P B) Min R = 3N + 25M + P C) Max R = 45N + 400M + 20P D) Min R = 3N + 25M + 20P E) Max R = 3N + 400M + 20P

67) A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). Which of the following is the constraint that limits the amount of time the writer will work each week? A) 3N + 25M + P ≥ 45 B) 3N + 25M + P ≤ 45 C) 3N + 25M + P ≤ 7 D) 45N + 400M + 20P ≤ 45 E) 45N + 400M + 20P ≥ 45 68) A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). What is the optimal mix of jobs for the writer to accept each week? A) N = 13, M = 0, P = 6 B) N = 12, M = 0, P = 7 C) N = 6, M = 1, P = 2 D) N = 5, M = 1, P = 5 E) N = 6, M = 1, P = 0

69) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. The manager's problem falls within which classification? A) Resource-allocation B) Cost-benefit-trade-off C) Mixed problems D) Transportation problems E) Assignment problems 70) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. Which of the following is the objective function for the grocer's problem? A) Max P = 1.5M + 2.5C + 3B B) Min P = 1.5M + 2.5C + 3B C) Max P = 2.5M + 1.5C + 3B D) Max P = 2.5M + 3C + 1.5B E) Min P = 1.5M + 1.5C + 3B 71) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. Which of the following is the constraint that limits the amount of milk the store will use (both in bundles and sold separately) each day? A) M + B ≥ 100 B) M + B ≤ 100 C) M + B ≥ 75 D) M + B ≤ 75 E) M ≤ 100

72) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. What is the maximum daily profit that the grocery store can achieve? A) $515 B) $485 C) $455 D) $425 E) $395 73) A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs per unit Plant A B C D

1 $ $ $ $

Customer 2 25 $ 35 20 $ 30 40 $ 35 15 $ 20

3 $ $ $ $

15 40 20 25

74) A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs per unit Plant A B C D

1 $ $ $ $

Customer 2 25 $ 35 20 $ 30 40 $ 35 15 $ 20

3 $ $ $ $

15 40 20 25

The firm needs to satisfy all demand each day, but would like to minimize the total costs. The objective function for the firm's problem will have how many terms? A) 5 B) 7 C) 10 D) 12 E) 14 75) A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs per unit Plant A B C D

Customer 1 2 $ 25 $ 35 $ 20 $ 30 $ 40 $ 35 $ 15 $ 20

3 $ $ $ $

15 40 20 25

76) A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs per unit Plant A B C D

1 $ $ $ $

Customer 2 25 $ 35 20 $ 30 40 $ 35 15 $ 20

3 $ $ $ $

15 40 20 25

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 3 Linear Programming: Formulation and Applications 1) When formulating a linear programming model on a spreadsheet, the decisions to be made are located in the data cells. Answer: FALSE Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the four components of any linear programming model and the kind of spreadsheet cells used for each component. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) When formulating a linear programming model on a spreadsheet, the constraints are located (in part) in the output cells. Answer: TRUE Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the four components of any linear programming model and the kind of spreadsheet cells used for each component. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) When formulating a linear programming model on a spreadsheet, the measure of performance is located in the objective cell. Answer: TRUE Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the four components of any linear programming model and the kind of spreadsheet cells used for each component. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

4) A mathematical model will be an exact representation of the real problem. Answer: FALSE Difficulty: 2 Medium Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 5) Approximations and simplifying assumptions generally are required to have a workable model. Answer: TRUE Difficulty: 2 Medium Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 6) Linear programming does not permit fractional solutions. Answer: FALSE Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) When formulating a linear programming problem on a spreadsheet, data cells will show the levels of activities for the decisions being made. Answer: FALSE Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the four components of any linear programming model and the kind of spreadsheet cells used for each component. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

8) A key assumption of linear programming is that the equation for each of the output cells, including the objective cell, can be expressed as a SUMPRODUCT (or SUM) function. Answer: TRUE Difficulty: 2 Medium Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the kinds of Excel functions that linear programming spreadsheet models use for the output cells, including the objective cell. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 9) Resource-allocation problems are linear programming problems involving the allocation of limited resources to activities. Answer: TRUE Difficulty: 1 Easy Topic: Resource-allocation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) Strict inequalities (i.e., < or >) are not permitted in linear programming formulations. Answer: TRUE Difficulty: 2 Medium Topic: Resource-allocation problems Learning Objective: Describe the difference between resource constraints and benefit constraints, including the difference in how they arise. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 11) When studying a resource-allocation problem, it is necessary to determine the contribution per unit of each activity to the overall measure of performance. Answer: TRUE Difficulty: 1 Easy Topic: Resource-allocation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

12) It is usually quite simple to obtain estimates of parameters in a linear programming problem. Answer: FALSE Difficulty: 2 Medium Topic: Model formulation from a broader perspective Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 13) The objective cell is a special kind of output cell. Answer: TRUE Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the kinds of Excel functions that linear programming spreadsheet models use for the output cells, including the objective cell. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) Financial planning is one of the most important areas of application for cost-benefit-tradeoff problems. Answer: FALSE Difficulty: 1 Easy Topic: Cost-benefit-trade-off problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) A resource constraint refers to any functional constraint with a ≥ sign in a linear programming model. Answer: FALSE Difficulty: 1 Easy Topic: Resource-allocation problems Learning Objective: Describe the difference between resource constraints and benefit constraints, including the difference in how they arise. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

16) In the algebraic form of a resource constraint, the coefficient of each decision variable is the resource usage per unit of the corresponding activity. Answer: TRUE Difficulty: 2 Medium Topic: Resource-allocation problems Learning Objective: Describe the difference between resource constraints and benefit constraints, including the difference in how they arise. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 17) Cost-benefit-tradeoff problems are linear programming problems involving the allocation of limited resources to activities. Answer: FALSE Difficulty: 1 Easy Topic: Cost-benefit-trade-off problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) For cost-benefit-tradeoff problems, minimum acceptable levels for each kind of benefit are prescribed and the objective is to achieve all these benefits with minimum cost. Answer: TRUE Difficulty: 2 Medium Topic: Cost-benefit-trade-off problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 19) A benefit constraint refers to a functional constraint with a ≥ sign in a linear programming model. Answer: TRUE Difficulty: 1 Easy Topic: Cost-benefit-trade-off problems Learning Objective: Describe the difference between resource constraints and benefit constraints, including the difference in how they arise. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 5 Copyright © 2019 McGraw-Hill

20) In most cases, the minimum acceptable level for a cost-benefit-tradeoff problem is set by how much money is available. Answer: FALSE Difficulty: 2 Medium Topic: Cost-benefit-trade-off problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 21) It is the nature of the application that determines the classification of the resulting linear programming formulation. Answer: FALSE Difficulty: 2 Medium Topic: Model formulation from a broader perspective Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) It is the nature of the restrictions imposed on the decisions regarding the mix of activity levels that determines the classification of the resulting linear programming formulation. Answer: TRUE Difficulty: 2 Medium Topic: Model formulation from a broader perspective Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) It is fairly common to have both resource constraints and benefit constraints in the same formulation. Answer: TRUE Difficulty: 1 Easy Topic: Mixed problems Learning Objective: Describe the difference between resource constraints and benefit constraints, including the difference in how they arise. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6 Copyright © 2019 McGraw-Hill

24) Choosing the best tradeoff between cost and benefits is a managerial judgment decision. Answer: TRUE Difficulty: 2 Medium Topic: Cost-benefit-trade-off problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 25) Having one requirement for each location is a characteristic common to all transportation problems. Answer: TRUE Difficulty: 1 Easy Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) Fixed-requirement constraints in a linear programming model are functional constraints that use an equal sign. Answer: TRUE Difficulty: 1 Easy Topic: Mixed problems Learning Objective: Describe fixed-requirement constraints and where they arise. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) The capacity row in a distribution-network formulation shows the maximum number of units than can be shipped through the network. Answer: FALSE Difficulty: 1 Easy Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

28) Once a linear programming problem has been formulated, it is rare to make major adjustments to it. Answer: FALSE Difficulty: 1 Easy Topic: Model formulation from a broader perspective Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 29) A mixed linear programming problem will always contain some of each of the three types of constraints in it. Answer: FALSE Difficulty: 2 Medium Topic: Mixed problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) Blending problems are a special type of mixed linear programming problems. Answer: TRUE Difficulty: 1 Easy Topic: Mixed problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) Model formulation should precede problem formulation. Answer: FALSE Difficulty: 2 Medium Topic: Model formulation from a broader perspective Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

32) When dealing with huge real problems, there is no such thing as the perfectly correct linear programming model for the problem. Answer: TRUE Difficulty: 1 Easy Topic: Model formulation from a broader perspective Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 33) Transportation problems are concerned with distributing commodities from sources to destinations in such a way as to minimize the total distribution cost. Answer: TRUE Difficulty: 1 Easy Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 34) Transportation problems always involve shipping goods from one location to another. Answer: FALSE Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) The requirements assumption states that each source has a fixed supply of units, where the entire supply must be distributed to the destinations and that each destination has a fixed demand for units, where the entire demand must be received from the sources. Answer: TRUE Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 9 Copyright © 2019 McGraw-Hill

36) A transportation problem requires a unit cost for every source-destination combination. Answer: TRUE Difficulty: 1 Easy Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 37) An assignment problem is a special type of transportation problem. Answer: TRUE Difficulty: 1 Easy Topic: Assignment problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) Generally, assignment problems match people to an equal number of tasks at a minimum cost. Answer: TRUE Difficulty: 1 Easy Topic: Assignment problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 39) A transportation problem will always return integer values for all decision variables. Answer: TRUE Difficulty: 1 Easy Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

40) In an assignment problem, it is necessary to add an integer constraint to the decision variables to ensure that they will take on a value of either 0 or 1. Answer: FALSE Difficulty: 1 Easy Topic: Assignment problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 41) A linear programming problem may return fractional solutions (e.g. 4 1/3) for a resource allocation problem. Answer: TRUE Difficulty: 1 Easy Topic: Resource-allocation problems Learning Objective: Recognize various kinds of managerial problems to which linear programming can be applied. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 42) In a cost-benefit-trade-off problem, management defines the maximum amount that can be spent and the objective is to maximize benefits within this cost target. Answer: FALSE Difficulty: 2 Medium Topic: Cost-benefit-trade-off problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 43) Transportation and assignment problems are examples of fixed-requirement problems. Answer: TRUE Difficulty: 1 Easy Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

44) A transportation problem with 3 factories and 4 customers will have 12 shipping lanes. Answer: TRUE Explanation: A transportation problem with m shipping nodes and n receiving nodes will have m×n shipping lanes. 3 × 4 = 12. Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 45) A transportation problem with 3 factories and 4 customers will have 12 fixed-requirement constraints. Answer: FALSE Explanation: A transportation problem with m shipping nodes and n receiving nodes will have m + n fixed-requirement constraints. 3 + 4 = 7. Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 46) Which of the following are categories of linear programming problems? A) Resource-allocation problems. B) Cost-benefit-tradeoff problems. C) Distribution-network problems. D) All of the above. E) None of the above. Answer: D Difficulty: 1 Easy Topic: Resource-allocation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

47) A linear programming model contains which of the following components? A) Data. B) Decisions. C) Constraints. D) Measure of performance. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the four components of any linear programming model and the kind of spreadsheet cells used for each component. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 48) In linear programming formulations, it is possible to have the following types of constraints: A) ≤. B) >. C) =. D) ≤ and > only. E) All of the answer choices are correct. Answer: E Difficulty: 2 Medium Topic: Model formulation from a broader perspective Learning Objective: Recognize various kinds of managerial problems to which linear programming can be applied. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 49) Resource-allocation problems have the following type of constraints: A) ≥. B) ≤. C) =. D) <. E) None of the answer choices are correct. Answer: B Difficulty: 1 Easy Topic: Resource-allocation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 13 Copyright © 2019 McGraw-Hill

50) When formulating a linear programming problem on a spreadsheet, which of the following is true? A) Parameters are called data cells. B) Decision variables are called changing cells. C) Right hand sides are part of the constraints. D) The objective function is called the objective cell. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: A case study: the super grain corp. advertising-mix problem Learning Objective: Identify the four components of any linear programming model and the kind of spreadsheet cells used for each component. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 51)

Where are data cells located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10 Answer: B Difficulty: 2 Medium Topic: Resource-allocation problems Learning Objective: Identify the kinds of Excel functions that linear programming spreadsheet models use for the output cells, including the objective cell. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

52)

Where are the changing cells located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10 Answer: C Difficulty: 2 Medium Topic: Resource-allocation problems Learning Objective: Identify the kinds of Excel functions that linear programming spreadsheet models use for the output cells, including the objective cell. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

53)

Where is the objective cell located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10 Answer: E Difficulty: 2 Medium Topic: Resource-allocation problems Learning Objective: Identify the kinds of Excel functions that linear programming spreadsheet models use for the output cells, including the objective cell. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

54)

Where are the output cells located? A) B2:D2 B) B2:D2, B4:D7, and G5:G7 C) B10:D10 D) E5:E7 E) G10 Answer: D Difficulty: 2 Medium Topic: Resource-allocation problems Learning Objective: Identify the kinds of Excel functions that linear programming spreadsheet models use for the output cells, including the objective cell. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 55) Cost-benefit tradeoff problems have the following type of constraints: A) ≥ B) ≤ C) = D) < E) None of the answer choices are correct. Answer: A Difficulty: 1 Easy Topic: Cost-benefit-trade-off problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

56) Mixed problems may have the following type of constraints: A) ≥. B) ≤. C) =. D) All of the answer choices are correct. E) None of the answer choices are correct. Answer: D Difficulty: 1 Easy Topic: Mixed problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 57) A linear programming problem where the objective is to find the best mix of ingredients for a product to meet certain specifications is called: A) a resource-allocation problem. B) a blending problem. C) a cost-benefit tradeoff problem. D) a mixture problem. E) None of the answer choices are correct. Answer: B Difficulty: 2 Medium Topic: Mixed problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

58) Using techniques to test the initial versions of a model to identify errors and omissions is called: A) model validation. B) model enrichment. C) model enhancement. D) model debugging. E) None of the answer choices are correct. Answer: A Difficulty: 1 Easy Topic: Model formulation from a broader perspective Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 59) Starting with a simple version of a model and adding to it until it reflects the real problem is called: A) model validation. B) model enrichment. C) model enhancement. D) model elaboration. E) None of the answer choices are correct. Answer: B Difficulty: 1 Easy Topic: Model formulation from a broader perspective Learning Objective: Understand the flexibility that managers have in prescribing key considerations that can be incorporated into a linear programming model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

60) The transportation model method for evaluating location alternatives minimizes: A) the number of sources. B) the number of destinations. C) total supply. D) total demand. E) total shipping cost. Answer: E Difficulty: 1 Easy Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 61) Which of the following is not information needed to use the transportation model? A) Capacity of the sources. B) Demand of the destinations. C) Unit shipping costs. D) Unit shipping distances. E) All of the answer choices are correct. Answer: D Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 62) When formulating a transportation problem on a spreadsheet, which of the following are necessary? A) A table of data. B) A network representation. C) A table for the solution. D) A table of data and a table for the solution only. E) All of the answer choices are correct. Answer: D Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 20 Copyright © 2019 McGraw-Hill

63) An assignment problem: A) is a special transportation problem. B) will always have an integer solution. C) has all supplies and demands equal to 1. D) None of the answer choices are correct. E) All of the answer choices are correct. Answer: E Difficulty: 2 Medium Topic: Assignment problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 64) Applications of assignment problems may include: A) matching personnel to jobs. B) assigning machines to tasks. C) designing bussing routes. D) matching personnel to jobs and assigning machines to tasks only. E) matching personnel to jobs, assigning machines to tasks, and designing bussing routes. Answer: E Difficulty: 2 Medium Topic: Assignment problems Learning Objective: Describe the five major categories of linear programming problems, including their identifying features. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

66) A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). Which of the following is the objective function for the writer's problem? A) Max R = 45N + 400M − 20P B) Min R = 3N + 25M + P C) Max R = 45N + 400M + 20P D) Min R = 3N + 25M + 20P E) Max R = 3N + 400M + 20P Answer: C Difficulty: 2 Medium Topic: Resource-allocation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

68) A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). What is the optimal mix of jobs for the writer to accept each week? A) N = 13, M = 0, P = 6 B) N = 12, M = 0, P = 7 C) N = 6, M = 1, P = 2 D) N = 5, M = 1, P = 5 E) N = 6, M = 1, P = 0 Answer: D Difficulty: 3 Hard Topic: Resource-allocation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

69) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. The manager's problem falls within which classification? A) Resource-allocation B) Cost-benefit-trade-off C) Mixed problems D) Transportation problems E) Assignment problems Answer: C Difficulty: 2 Medium Topic: Mixed problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 70) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. Which of the following is the objective function for the grocer's problem? A) Max P = 1.5M + 2.5C + 3B B) Min P = 1.5M + 2.5C + 3B C) Max P = 2.5M + 1.5C + 3B D) Max P = 2.5M + 3C + 1.5B E) Min P = 1.5M + 1.5C + 3B Answer: A Difficulty: 2 Medium Topic: Mixed problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 26 Copyright © 2019 McGraw-Hill

71) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. Which of the following is the constraint that limits the amount of milk the store will use (both in bundles and sold separately) each day? A) M + B ≥ 100 B) M + B ≤ 100 C) M + B ≥ 75 D) M + B ≤ 75 E) M ≤ 100 Answer: B Difficulty: 2 Medium Topic: Mixed problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 72) A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. What is the maximum daily profit that the grocery store can achieve? A) $515 B) $485 C) $455 D) $425 E) $395 Answer: A Difficulty: 2 Medium Topic: Mixed problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Apply AACSB: Analytical Thinking 27 Copyright © 2019 McGraw-Hill

73) A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs per unit Plant A B C D

1 $ $ $ $

Customer 2 25 $ 35 20 $ 30 40 $ 35 15 $ 20

3 $ $ $ $

15 40 20 25

The firm needs to satisfy all demand each day, but would like to minimize the total costs. The firm's problem falls within which classification? A) Resource-allocation B) Cost-benefit-trade-off C) Transshipment problems D) Transportation problems E) Assignment problems Answer: D Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

1 $ $ $ $

Customer 2 25 $ 35 20 $ 30 40 $ 35 15 $ 20

3 $ $ $ $

15 40 20 25

The firm needs to satisfy all demand each day, but would like to minimize the total costs. The objective function for the firm's problem will have how many terms? A) 5 B) 7 C) 10 D) 12 E) 14 Answer: D Difficulty: 2 Medium Topic: Transportation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

75) A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs per unit Plant A B C D

1 $ $ $ $

Customer 2 25 $ 35 20 $ 30 40 $ 35 15 $ 20

3 $ $ $ $

15 40 20 25

The firm needs to satisfy all demand each day, but would like to minimize the total costs. Which of the following constraints is unnecessary for this problem (xi,j is the number of widgets shipped from factory i to customer j)? A) xA,1 + xA,2 + xA,3 ≤ 100 B) xB,1 + xB,2 + xB,3 ≤ 100 C) xC,1 + xxC,2 + xxC,3 ≤ 100 D) xA,1 + xB,1 + xxC,1 ≤ 75 E) xA,1, xA,2, xA,3, xB,1, xB,2, xB,3, xC,1, xC,2, xC,3 integer Answer: E Difficulty: 3 Hard Topic: Transportation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

1 $ $ $ $

Customer 2 25 $ 35 20 $ 30 40 $ 35 15 $ 20

3 $ $ $ $

15 40 20 25

The firm needs to satisfy all demand each day, but would like to minimize the total costs. What is the minimum daily shipping cost that the firm can achieve? A) $6,725 B) $7,125 C) $7,525 D) $7,925 E) $8,325 Answer: B Difficulty: 3 Hard Topic: Transportation problems Learning Objective: Formulate a linear programming model from a description of a problem in any of these categories. Bloom's: Analyze AACSB: Analytical Thinking

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 4 The Art of Modeling with Spreadsheets 1) If two managers are given the same business problem to analyze with a spreadsheet, their spreadsheet models will likely be almost identical. 2) There is a systematic procedure that will lead to a single correct spreadsheet model. 3) The Plan-Build-Test-Analyze process should always be followed step-by-step, from beginning to end: Plan then Build then Test then Analyze. 4) When building a model, it is often a good idea to start with a small-scale version of the problem. 5) When sketching out a spreadsheet, it is important to have selected the formulas for all of the output cells. 6) An absolute reference does not change when it is filled or copied into other cells. 7) A relative reference does not change when it is filled or copied into other cells. 8) The data is the first thing that should be entered in a spreadsheet model. 9) Once the data is entered into a spreadsheet model, it should never be moved. 10) Data (for example, prices or costs) should be entered directly into every output cell as needed. 11) When a number is needed in an output cell, it should typically be entered there directly. 12) It is better to use powerful functions in Excel to complete a calculation in a single cell than to spread out a calculation over many cells using simpler formulas. 13) Whenever possible, the entire model should be displayed on the spreadsheet. 14) Colors and shading should be avoided on a spreadsheet because it distracts from the model. 15) The toggle feature in Excel switches back and forth between viewing formulas and viewing values in the output cells. 16) The auditing tools can be used to trace the cells that make reference to a particular cell. 17) Numbers should be included directly in formulas rather than entered separately in data cells in order to keep the spreadsheet model concise. 18) If you add rows or columns to a spreadsheet Excel will automatically adjust named ranges to compensate.

19) In the example shown below, cell B4 is an input to cell B7.

20) In the example shown below, cells B7 through B18 are inputs to cell B4.

21) In the example shown below, cell C7 uses absolute reference.

22) In the example shown below, cell B3 is a data cell.

23) In the example shown below, cell B2 uses an Excel formula.

24) In the example shown below, cell D7 uses absolute reference.

25) When developing a new spreadsheet model, it is important to first get a model that works and then to go back later and change the layout so the model is easy to read. 26) The first step in spreadsheet building is to enter the formulas into their proper cells. 27) An absolute reference changes when it is filled or copied into other cells. 28) A relative reference changes when it is filled or copied into other cells. 29) Colors and shading can be used to make a spreadsheet model much easier to read and interpret. 30) The auditing tools can be used to determine which user last made changes to a particular cell. 31) Which of the following is not a major step in the process of modeling with spreadsheets? A) Plan. B) Build. C) Test. D) Analyze. E) All of the answer choices are major steps. 32) Which of the following best describes spaghetti code? A) Code that is not logically organized and jumps all over the place. B) Code that is well documented. C) Code that has a clear beginning, middle, and end. D) All of the answer choices are correct. E) None of the answer choices are correct.

33) Which of the following is not a part of the planning step when building a spreadsheet model? A) Visualize where you want to finish. B) Do some calculations by hand. C) Sketch out a spreadsheet. D) Test the spreadsheet model. E) All of the answer choices are part of the planning step. 34) Which of the following is an appropriate first step when building a spreadsheet model? A) Start with building a small scale model. B) Visualize where you want to finish. C) Test the model. D) Expand the model to full scale. E) Optimize the model. 35) Which of the following tips can be helpful when you can't figure out what formula needs to be entered in an output cell? A) Visualize where you want to finish. B) Test the model. C) Do some calculations by hand. D) Optimize the model. E) All of the answer choices are correct. 36) When testing a spreadsheet model by entering values in the changing cells, which of the following are appropriate values to enter? A) Zeroes. B) Values for which you know what the values of the output cells should be. C) Large numbers. D) Zeros, large numbers, and inputs for which you know what the values of the output cells should be. E) All of the answer choices are correct. 37) Which of the following should be entered first when building a spreadsheet model? A) The objective cell. B) The data cells. C) The changing cells. D) The output cells. E) The Solver parameters. 38) Which of the following are valid range names in Excel? A) Total Profit B) TotalProfit C) Total_Profit D) All of the answer choices are correct. E) TotalProfit and Total_Profit only.

39) Which of the following is not an advantage of using range names? A) They make formulas easier to interpret. B) They make the Solver entries easier to understand. C) They make the model easier to modify. D) They make the Solver entries easier to understand and they make the model easier to modify are not advantages of using range names. E) All of the answer choices are advantages of using range names. 40) How many cells should be used to represent each constraint? A) 0 B) 1 C) 2 D) 3 E) 4 41) Each data value should be entered into how many cells? A) 0 B) 1 C) 2 D) 3 E) The value should be entered into any formula in which it is needed. 42) Which of the following can be done using the auditing tools in Excel? A) Trace the cells that make reference to a particular cell. B) Trace the cells that a particular cell refers to. C) Trace the history of values for a particular cell. D) Determine the valid entries in a particular cell. E) Trace the cells that make reference to a particular cell and trace the cells that a particular cell refers to only. 43) Which of the following are ways to distinguish data cells, changing cells, output cells, and the objective cell on a spreadsheet? A) Borders. B) Shading. C) Color. D) All of the answer choices are correct. E) Borders and color only. 44) Which of the following actions will toggle the worksheet between viewing values and formulas? A) Pressing Ctrl+~ on a PC. B) Pressing Command+~ on a Mac. C) Selecting the auditing tools to Trace Dependents. D) Pressing Ctrl+~ on a PC and pressing Command+~ on a Mac. E) Pressing Ctrl+~ on a PC, pressing Command+~ on a Mac, and selecting the auditing tools to Trace Dependents.

45) In the spreadsheet shown below, changing the value in Cell B1 will cause which other cells to change?

A) Cell B2. B) Cell B3. C) Cell B7. D) Cell D18. E) None of the answer choices are correct.

46) In the spreadsheet shown below, which of the following is NOT a data cell?

A) Cell B1. B) Cell B2. C) Cell B3. D) Cell B7. E) All of the answer choices are data cells. 47) Before staring work on a spreadsheet, Julie sketches a rough draft of how the finished spreadsheet might look. Julie is performing which step of the modeling process? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. 48) Before building a full-scale version of her spreadsheet model, Julie constructs a smaller version of the spreadsheet. Julie is performing which step of the modeling process? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. 9 Copyright © 2019 McGraw-Hill

49) When an analyst enters data into a model to see if the results match expectations, which step of the modeling process is occurring? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. 50) When an analyst uses Solver to find the optimal solution to a problem modeled on a spreadsheet, which step in the modeling process is occurring? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. 51) A college student is developing a spreadsheet model of a budget. To calculate the monthly surplus (or deficit), the student subtracts living expenses, entertainment costs, and savings from income. Entering which of the following formulas into cell B5 will perform the proper calculation?

A) =Monthly Income − Expenses B) =B1 − B2 − B3 − B4 C) =B2 + B3 + B4 − B1 D) =B1 + (B2 − B3 − B4) E) =B1 − (B2 − B3 − B4)

52) After pressing Ctrl+~ to toggle Excel to view formulas, an analyst reviews the spreadsheet shown below. Which of the following is TRUE?

A) Cell B2 is a data cell. B) Cell B3 is a formula cell. C) Cell B6 is a data cell. D) Cell B6 is a formula cell. E) Only A and D are true. 53) A student is using a spreadsheet model to track monthly income and expenses and also to calculate his annual income. After pressing Ctrl+~, the formula view of the spreadsheet (shown below) was visible. What spreadsheet construction error did the student commit?

54) A student is using a spreadsheet to calculate her monthly surplus/deficit as well as annual income. After pressing Ctrl+~, the formula view (shown below) appeared. What issues should be addressed on this spreadsheet?

A) Data should be entered only once. B) Simple formulas should be used rather than complex Excel functions. C) Range names should be used. D) Absolute references should be used. E) No problems exist on this spreadsheet. 55) A manager prepared a spreadsheet to calculate employee wages. After pressing Ctrl+~, the formula view (shown below) appeared. What issues should be addressed on this spreadsheet?

56) A spreadsheet developer enters the formula "=B9*B10" into cell C1. If this formula is copied and then pasted into cell C2, what will the formula in cell C2 be? A) =B9*B10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =B10*B11 57) A spreadsheet developer enters the formula "=$B$9*$B$10" into cell C1. If this formula is copied and then pasted into cell C2, what will the formula in cell C2 be? A) =$B$9*$B$10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =$B$10*$B$11 58) A spreadsheet developer enters the formula "=B9*B10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =B9*B10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =B10*B11 59) A spreadsheet developer enters the formula "=$B$9*$B$10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =$B$9*$B$10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =$B$10*$B$11 60) A spreadsheet developer enters the formula "=B9*$B$10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =B9*$B$10 B) =C9*C10 C) =$C$10*$C$11 D) =B9*$B$11 E) =C10*$B$10 61) A spreadsheet developer enters the formula "=$B$9*B10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =$B$9*B10 B) =$B$9*C11 C) =C10*C11 D) =B9*B11 E) =$B$10*$B$11 13 Copyright © 2019 McGraw-Hill

62) Which of the following are valid range names in Excel? A) Unit_Cost B) Unit Cost C) Cost per Unit D) All of the answer choices are correct. E) Unit Cost and Cost per Unit only. 63) In the spreadsheet shown below, which of the following is a data cell?

A) Cell B1. B) Cell B7. C) Cell D7. D) Cell D18. E) All of the answer choices are data cells.

64) Which of the following statements is TRUE about a good spreadsheet model? A) A good model is easy to understand. B) A good model is easy to debug. C) A good model is difficult for users to modify. D) A good model doesn't use borders and shading. E) A good model is easy to understand and a good model is easy to debug. 65) Which of the following statements about a good spreadsheet model is FALSE? A) A good model is easy to understand. B) A good model is easy to debug. C) A good model is easy to modify. D) A good model doesn't use borders and shading. E) A good model is easy to understand and a good model is easy to debug. 66) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After entering the data below, the modeler would like to enter a formula in cell C5 that can then be copied to cells C6 through C9 without further modification. What formula should be entered in cell C5 to make this possible?

A) =B2*B5 B) =B2*$B$5 C) =$B$2*B5 D) =$B$2*$B$5 E) =B2+B5

67) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. The modeler has named cell B2 "Hourly_Wage" to make the model more understandable. What formula should be entered into cell C5?

A) =B1*B5 B) =B1*$B$5 C) =Hourly_Wage*B5 D) =$B$2*Hourly_Wage E) =Hourly_Wage +B5 68) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After completing the model, the analyst feels there is an error. Interpret the auditing information shown below to determine which of the following statements is TRUE.

69) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After completing the model, the analyst feels there is an error. Interpret the auditing information shown below to determine which of the following statements is TRUE.

71) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After completing the model, the analyst feels there is an error. Interpret the auditing information shown below to determine which of the following statements is TRUE.

73) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After completing the model, the analyst feels there is an error. Interpret the formula information shown below to determine which of the following statements is TRUE.

A) There is no error in the model. B) The model is incorrect because it is using the wrong information for the employee hours. C) The model is incorrect because it is using the wrong wage information. D) The model is incorrect, but it is impossible to determine why. E) The model is incorrect because it is using the wrong information for the employee hours and the model is incorrect because it is using the wrong wage information are both true. 74) Which of the following statements about a "good" spreadsheet model is FALSE? A) A good model is easy to understand. B) A good model will always give the correct result. C) A good model is easy to modify. D) A good model has data entered in only one location. E) A good model uses range names to make formulas easier to understand. 75) Which of the following statements about a "poor" spreadsheet model is FALSE? A) A poor model is easy to understand. B) A poor model will always give an incorrect result. C) A poor model is easy to modify. D) A poor model has data entered in only one location. E) A poor model uses range names to make formulas easier to understand.

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 4 The Art of Modeling with Spreadsheets 1) If two managers are given the same business problem to analyze with a spreadsheet, their spreadsheet models will likely be almost identical. Answer: FALSE Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) There is a systematic procedure that will lead to a single correct spreadsheet model. Answer: FALSE Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) The Plan-Build-Test-Analyze process should always be followed step-by-step, from beginning to end: Plan then Build then Test then Analyze. Answer: FALSE Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) When building a model, it is often a good idea to start with a small-scale version of the problem. Answer: TRUE Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

5) When sketching out a spreadsheet, it is important to have selected the formulas for all of the output cells. Answer: FALSE Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) An absolute reference does not change when it is filled or copied into other cells. Answer: TRUE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) A relative reference does not change when it is filled or copied into other cells. Answer: FALSE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) The data is the first thing that should be entered in a spreadsheet model. Answer: TRUE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

9) Once the data is entered into a spreadsheet model, it should never be moved. Answer: FALSE Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) Data (for example, prices or costs) should be entered directly into every output cell as needed. Answer: FALSE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) When a number is needed in an output cell, it should typically be entered there directly. Answer: FALSE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) It is better to use powerful functions in Excel to complete a calculation in a single cell than to spread out a calculation over many cells using simpler formulas. Answer: FALSE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) Whenever possible, the entire model should be displayed on the spreadsheet. Answer: TRUE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) Colors and shading should be avoided on a spreadsheet because it distracts from the model. Answer: FALSE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) The toggle feature in Excel switches back and forth between viewing formulas and viewing values in the output cells. Answer: TRUE Difficulty: 1 Easy Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) The auditing tools can be used to trace the cells that make reference to a particular cell. Answer: TRUE Difficulty: 1 Easy Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

17) Numbers should be included directly in formulas rather than entered separately in data cells in order to keep the spreadsheet model concise. Answer: FALSE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) If you add rows or columns to a spreadsheet Excel will automatically adjust named ranges to compensate. Answer: FALSE Difficulty: 2 Medium Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

19) In the example shown below, cell B4 is an input to cell B7.

Answer: TRUE Difficulty: 2 Medium Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

20) In the example shown below, cells B7 through B18 are inputs to cell B4.

Answer: FALSE Difficulty: 2 Medium Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

21) In the example shown below, cell C7 uses absolute reference.

Answer: TRUE Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

22) In the example shown below, cell B3 is a data cell.

23) In the example shown below, cell B2 uses an Excel formula.

24) In the example shown below, cell D7 uses absolute reference.

Answer: FALSE Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 25) When developing a new spreadsheet model, it is important to first get a model that works and then to go back later and change the layout so the model is easy to read. Answer: FALSE Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) The first step in spreadsheet building is to enter the formulas into their proper cells. Answer: FALSE Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 11 Copyright © 2019 McGraw-Hill

27) An absolute reference changes when it is filled or copied into other cells. Answer: FALSE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) A relative reference changes when it is filled or copied into other cells. Answer: TRUE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 29) Colors and shading can be used to make a spreadsheet model much easier to read and interpret. Answer: TRUE Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) The auditing tools can be used to determine which user last made changes to a particular cell. Answer: FALSE Difficulty: 1 Easy Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

31) Which of the following is not a major step in the process of modeling with spreadsheets? A) Plan. B) Build. C) Test. D) Analyze. E) All of the answer choices are major steps. Answer: E Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 32) Which of the following best describes spaghetti code? A) Code that is not logically organized and jumps all over the place. B) Code that is well documented. C) Code that has a clear beginning, middle, and end. D) All of the answer choices are correct. E) None of the answer choices are correct. Answer: A Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 33) Which of the following is not a part of the planning step when building a spreadsheet model? A) Visualize where you want to finish. B) Do some calculations by hand. C) Sketch out a spreadsheet. D) Test the spreadsheet model. E) All of the answer choices are part of the planning step. Answer: D Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

34) Which of the following is an appropriate first step when building a spreadsheet model? A) Start with building a small scale model. B) Visualize where you want to finish. C) Test the model. D) Expand the model to full scale. E) Optimize the model. Answer: B Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) Which of the following tips can be helpful when you can't figure out what formula needs to be entered in an output cell? A) Visualize where you want to finish. B) Test the model. C) Do some calculations by hand. D) Optimize the model. E) All of the answer choices are correct. Answer: C Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 36) When testing a spreadsheet model by entering values in the changing cells, which of the following are appropriate values to enter? A) Zeroes. B) Values for which you know what the values of the output cells should be. C) Large numbers. D) Zeros, large numbers, and inputs for which you know what the values of the output cells should be. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14 Copyright © 2019 McGraw-Hill

37) Which of the following should be entered first when building a spreadsheet model? A) The objective cell. B) The data cells. C) The changing cells. D) The output cells. E) The Solver parameters. Answer: B Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) Which of the following are valid range names in Excel? A) Total Profit B) TotalProfit C) Total_Profit D) All of the answer choices are correct. E) TotalProfit and Total_Profit only. Answer: E Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 39) Which of the following is not an advantage of using range names? A) They make formulas easier to interpret. B) They make the Solver entries easier to understand. C) They make the model easier to modify. D) They make the Solver entries easier to understand and they make the model easier to modify are not advantages of using range names. E) All of the answer choices are advantages of using range names. Answer: C Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

40) How many cells should be used to represent each constraint? A) 0 B) 1 C) 2 D) 3 E) 4 Answer: D Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 41) Each data value should be entered into how many cells? A) 0 B) 1 C) 2 D) 3 E) The value should be entered into any formula in which it is needed. Answer: B Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 42) Which of the following can be done using the auditing tools in Excel? A) Trace the cells that make reference to a particular cell. B) Trace the cells that a particular cell refers to. C) Trace the history of values for a particular cell. D) Determine the valid entries in a particular cell. E) Trace the cells that make reference to a particular cell and trace the cells that a particular cell refers to only. Answer: E Difficulty: 1 Easy Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

43) Which of the following are ways to distinguish data cells, changing cells, output cells, and the objective cell on a spreadsheet? A) Borders. B) Shading. C) Color. D) All of the answer choices are correct. E) Borders and color only. Answer: D Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 44) Which of the following actions will toggle the worksheet between viewing values and formulas? A) Pressing Ctrl+~ on a PC. B) Pressing Command+~ on a Mac. C) Selecting the auditing tools to Trace Dependents. D) Pressing Ctrl+~ on a PC and pressing Command+~ on a Mac. E) Pressing Ctrl+~ on a PC, pressing Command+~ on a Mac, and selecting the auditing tools to Trace Dependents. Answer: D Difficulty: 1 Easy Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

45) In the spreadsheet shown below, changing the value in Cell B1 will cause which other cells to change?

A) Cell B2. B) Cell B3. C) Cell B7. D) Cell D18. E) None of the answer choices are correct. Answer: D Explanation: The auditing tools show that cell B4 is dependent upon cell B1. Similarly, cell B18 depends upon B4, and D18 depends upon B18. Therefore, B1 influences D18. Cells B2, B3, and B7 are not dependent upon B1. Difficulty: 2 Medium Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

46) In the spreadsheet shown below, which of the following is NOT a data cell?

A) Cell B1. B) Cell B2. C) Cell B3. D) Cell B7. E) All of the answer choices are data cells. Answer: D Explanation: Cell B7 calculates the interest using the data from cells B2 and B3. Therefore, it is not a data cell but a formula cell. Cells B1, B2, and B3 are data cells. Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

47) Before staring work on a spreadsheet, Julie sketches a rough draft of how the finished spreadsheet might look. Julie is performing which step of the modeling process? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. Answer: A Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 48) Before building a full-scale version of her spreadsheet model, Julie constructs a smaller version of the spreadsheet. Julie is performing which step of the modeling process? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. Answer: B Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 49) When an analyst enters data into a model to see if the results match expectations, which step of the modeling process is occurring? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. Answer: C Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 20 Copyright © 2019 McGraw-Hill

50) When an analyst uses Solver to find the optimal solution to a problem modeled on a spreadsheet, which step in the modeling process is occurring? A) Plan. B) Build. C) Test. D) Analyze. E) None of the answer choices are correct. Answer: D Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 51) A college student is developing a spreadsheet model of a budget. To calculate the monthly surplus (or deficit), the student subtracts living expenses, entertainment costs, and savings from income. Entering which of the following formulas into cell B5 will perform the proper calculation?

A) =Monthly Income − Expenses B) =B1 − B2 − B3 − B4 C) =B2 + B3 + B4 − B1 D) =B1 + (B2 − B3 − B4) E) =B1 − (B2 − B3 − B4) Answer: B Difficulty: 2 Medium Topic: Overview of the process of modeling with spreadsheets Learning Objective: Apply both the general process for modeling in spreadsheets and the guidelines in this chapter to develop your own spreadsheet model from a description of the problem. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 21 Copyright © 2019 McGraw-Hill

52) After pressing Ctrl+~ to toggle Excel to view formulas, an analyst reviews the spreadsheet shown below. Which of the following is TRUE?

A) Cell B2 is a data cell. B) Cell B3 is a formula cell. C) Cell B6 is a data cell. D) Cell B6 is a formula cell. E) Only A and D are true. Answer: E Difficulty: 2 Medium Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

53) A student is using a spreadsheet model to track monthly income and expenses and also to calculate his annual income. After pressing Ctrl+~, the formula view of the spreadsheet (shown below) was visible. What spreadsheet construction error did the student commit?

A) Using an advanced Excel formula instead of a simpler mathematical calculation. B) Entering data in more than one place. C) Failure to adequately use labels to identify cells. D) Incorrect formula. E) There are no errors in the spreadsheet. Answer: B Explanation: The data "monthly income" is entered in both cell B2 and B8. It should be entered in only one cell. Difficulty: 3 Hard Topic: Overview of the process of modeling with spreadsheets Learning Objective: Apply both the general process for modeling in spreadsheets and the guidelines in this chapter to develop your own spreadsheet model from a description of the problem. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

A) Data should be entered only once. B) Simple formulas should be used rather than complex Excel functions. C) Range names should be used. D) Absolute references should be used. E) No problems exist on this spreadsheet. Answer: C Explanation: Use of range names makes formulas more easily interpreted. Difficulty: 3 Hard Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Identify some deficiencies in a poorly formulated spreadsheet model. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

55) A manager prepared a spreadsheet to calculate employee wages. After pressing Ctrl+~, the formula view (shown below) appeared. What issues should be addressed on this spreadsheet?

A) Data should be entered only once. B) Simple formulas should be used rather than complex Excel functions. C) Absolute references should be used. D) Data should be entered only once and simple formulas should be used rather than complex Excel functions only. E) Data should be entered only once, simple formulas should be used rather than complex Excel functions and absolute references should be used. Answer: D Explanation: Data (wage per hour) should be entered only once. The Excel function "PRODUCT" is more complex than needed for this application. Simply multiplying the three cells together (e.g. =B9*B10*B11) is sufficient and more easily understood. Difficulty: 3 Hard Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Identify some deficiencies in a poorly formulated spreadsheet model. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 56) A spreadsheet developer enters the formula "=B9*B10" into cell C1. If this formula is copied and then pasted into cell C2, what will the formula in cell C2 be? A) =B9*B10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =B10*B11 Answer: E Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 25 Copyright © 2019 McGraw-Hill

57) A spreadsheet developer enters the formula "=$B$9*$B$10" into cell C1. If this formula is copied and then pasted into cell C2, what will the formula in cell C2 be? A) =$B$9*$B$10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =$B$10*$B$11 Answer: A Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 58) A spreadsheet developer enters the formula "=B9*B10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =B9*B10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =B10*B11 Answer: C Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 59) A spreadsheet developer enters the formula "=$B$9*$B$10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =$B$9*$B$10 B) =C9*C10 C) =C10*C11 D) =B9*B11 E) =$B$10*$B$11 Answer: A Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 26 Copyright © 2019 McGraw-Hill

60) A spreadsheet developer enters the formula "=B9*$B$10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =B9*$B$10 B) =C9*C10 C) =$C$10*$C$11 D) =B9*$B$11 E) =C10*$B$10 Answer: E Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 61) A spreadsheet developer enters the formula "=$B$9*B10" into cell C1. If this formula is copied and then pasted into cell D2, what will the formula in cell D2 be? A) =$B$9*B10 B) =$B$9*C11 C) =C10*C11 D) =B9*B11 E) =$B$10*$B$11 Answer: B Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 62) Which of the following are valid range names in Excel? A) Unit_Cost B) Unit Cost C) Cost per Unit D) All of the answer choices are correct. E) Unit Cost and Cost per Unit only. Answer: A Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 27 Copyright © 2019 McGraw-Hill

63) In the spreadsheet shown below, which of the following is a data cell?

A) Cell B1. B) Cell B7. C) Cell D7. D) Cell D18. E) All of the answer choices are data cells. Answer: A Difficulty: 2 Medium Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

64) Which of the following statements is TRUE about a good spreadsheet model? A) A good model is easy to understand. B) A good model is easy to debug. C) A good model is difficult for users to modify. D) A good model doesn't use borders and shading. E) A good model is easy to understand and a good model is easy to debug. Answer: E Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 65) Which of the following statements about a good spreadsheet model is FALSE? A) A good model is easy to understand. B) A good model is easy to debug. C) A good model is easy to modify. D) A good model doesn't use borders and shading. E) A good model is easy to understand and a good model is easy to debug. Answer: D Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe the general process for modeling in spreadsheets. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

66) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After entering the data below, the modeler would like to enter a formula in cell C5 that can then be copied to cells C6 through C9 without further modification. What formula should be entered in cell C5 to make this possible?

A) =B2*B5 B) =B2*$B$5 C) =$B$2*B5 D) =$B$2*$B$5 E) =B2+B5 Answer: C Difficulty: 3 Hard Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

A) =B1*B5 B) =B1*$B$5 C) =Hourly_Wage*B5 D) =$B$2*Hourly_Wage E) =Hourly_Wage +B5 Answer: C Difficulty: 3 Hard Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

68) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After completing the model, the analyst feels there is an error. Interpret the auditing information shown below to determine which of the following statements is TRUE.

70) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After completing the model, the analyst feels there is an error. Interpret the auditing information shown below to determine which of the following statements is TRUE.

72) A spreadsheet modeler is creating a spreadsheet to calculate each employee's total wages for a time period. After completing the model, the analyst feels there is an error. Interpret the auditing information shown below to determine which of the following statements is TRUE.

A) There is no error in the model. B) The model is incorrect because it is using the wrong information for the employee hours. C) The model is incorrect because it is using the wrong wage information. D) The model is incorrect, but it is impossible to determine why. E) The model is incorrect because it is using the wrong information for the employee hours and the model is incorrect because it is using the wrong wage information are both true. Answer: B Difficulty: 3 Hard Topic: Debugging a spreadsheet model Learning Objective: Apply a variety of techniques for debugging a spreadsheet model. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 74) Which of the following statements about a "good" spreadsheet model is FALSE? A) A good model is easy to understand. B) A good model will always give the correct result. C) A good model is easy to modify. D) A good model has data entered in only one location. E) A good model uses range names to make formulas easier to understand. Answer: B Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 37 Copyright © 2019 McGraw-Hill

75) Which of the following statements about a "poor" spreadsheet model is FALSE? A) A poor model is easy to understand. B) A poor model will always give an incorrect result. C) A poor model is easy to modify. D) A poor model has data entered in only one location. E) A poor model uses range names to make formulas easier to understand. Answer: B Difficulty: 1 Easy Topic: Some guidelines for building "good" spreadsheet models Learning Objective: Describe some guidelines for building good spreadsheet models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 5 What-If Analysis for Linear Programming 1) An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem. 2) The purpose of a linear programming study is to help guide management's final decision by providing insights. 3) It is usually quite easy to find the needed data for a linear programming study. 4) If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function, then management will want to take special care to narrow this estimate down. 5) Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem. 6) When certain parameters of a model represent managerial policy decisions, what-if analysis provides information about what the impact would be of altering these policy decisions. 7) The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity. 8) The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate. 9) A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint. 10) When maximizing profit in a linear programming problem, the allowable increase and allowable decrease columns in the sensitivity report make it possible to find the range over which the profitability does not change. 11) Changing the objective function coefficients may or may not change the optimal solution, but it will always change the value of the objective function. 12) Every change in the value of an objective function coefficient will lead to a changed optimal solution. 13) When a change in the value of an objective function coefficient remains within the allowable range, the optimal solution will also remain the same. 14) According to the 100% rule for simultaneous changes in objective function coefficients, if the sum of the percentage changes exceeds 100%, the optimal solution definitely will change.

15) Whenever proportional changes are made to all the unit profits in a problem, the optimal solution will remain the same. 16) The term "allowable range for the right-hand-side" refers to coefficients of the objective function. 17) If the change to a right-hand side is within the allowable range, the value of the shadow price remains valid. 18) If the change to a right-hand side is within the allowable range, the solution will remain the same. 19) A shadow price tells how much a decision variable can be increased or decreased without changing the value of the solution. 20) The allowable range gives ranges of values for the objective function coefficients within which the values of the decision variables are optimal. 21) When a change occurs in the right-hand side values of one of the constraints, a proportional change will occur in one of the coefficients of the objective function. 22) Managerial decisions regarding right-hand sides are often interrelated and so frequently are considered simultaneously. 23) If the sum of the percentage changes of the right-hand sides does not exceed 100%, then the solution will definitely remain optimal. 24) A parameter analysis report re-solves the problem for a range of values of a data cell. 25) A parameter analysis report can only be used to investigate changes in a single data cell at a time. 26) A parameter analysis report can be used to easily investigate the changes in any number of data cells. 27) A shadow price reflects which of the following in a maximization problem? A) The marginal cost of adding additional resources. B) The marginal gain in the objective value realized by adding one unit of a resource. C) The marginal loss in the objective value realized by adding one unit of a resource. D) The marginal gain in the objective value realized by subtracting one unit of a resource. E) None of the choices is correct.

28) In linear programming, what-if analysis is associated with determining the effect of changing: I. objective function coefficients. II. right-hand side values of constraints. III. decision variable values. A) objective function coefficients and right-hand side values of constraints. B) right-hand side values of constraints and decision variable values. C) objective function coefficients, right-hand side values of constraints, and decision variable values. D) objective function coefficients and decision variable values. E) None of the choices is correct. 29) What-if analysis can: I. be done graphically for problems with two decision variables. II. reduce a manager's confidence in the model that has been formulated. III. increase a manager's confidence in the model that has been formulated. A) I only. B) II only. C) III only. D) All of the these. E) I and III only. 30) What-if analysis: A) may involve changes in the objective function coefficients. B) requires that only one parameter change while the rest are held fixed. C) may involve changes in the right-hand side values. D) All of the choices are correct. E) None of the choices is correct. 31) If a change is made in only one of the objective function coefficients: A) the slope of the objective function line always will change. B) the optimal solution always will change. C) one or more of the decision variables always will change. D) All of the choices are correct. E) None of the choices is correct. 32) If the right-hand side value of a constraint in a two variable linear programming problems is changed, then: A) the optimal measure of performance may change. B) a parallel shift must be made in the graph of that constraint. C) the optimal values for one or more of the decision variables may change. D) All of the choices are correct. E) None of the choices is correct.

33) Which of the following are benefits of what-if analysis? A) It pinpoints the sensitive parameters of the model. B) It gives the new optimal solution if conditions change. C) It tells management what policy decisions to make. D) All of the choices are correct. E) None of the choices is correct. 34) When even a small change in the value of a coefficient in the objective function can change the optimal solution, the coefficient is called: A) optimal. B) sensitive. C) out of the range. D) within the range. E) None of the choices is correct. 35) In a problem with 4 decision variables, the 100% rule indicates that each objective coefficient can be safely increased by what amount without invalidating the current optimal solution? A) 25%. B) 25% of the allowable increase of that coefficient. C) 100%. D) 25% of the range of optimality. E) It can't be determined from the information given. 36) variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

What is the optimal objective function value for this problem? A) It cannot be determined from the given information. B) $7.78 C) $240 D) $90 E) $330

37) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

What is the allowable range for the objective coefficient for Activity 2? A) −10 ≤ A2 ≤ 50 B) −44 ≤ A2 ≤ 16 C) −4 ≤ A2 ≤ 56 D) 30 ≤ A2 ≤ 90 E) 20 ≤ A2 ≤ 80 38) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

What is the allowable range for the right-hand-side for Resource C? A) 18 ≤ RHSc ≤ ∞ B) ∞ ≤ RHSc ≤ 62 C) −2 ≤RHSc ≤ ∞ D) − ∞ ≤ RHSc ≤ 40 E) 0 ≤ RHSc ≤ 22

39) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

41) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

43) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 −7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

45) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the coefficients of Activity 1 and Activity 2 in the objective function are both increased by $10, then: A) the optimal solution remains the same. B) the optimal solution may or may not remain the same. C) the optimal solution will change. D) the shadow prices are valid. E) None of the choices is correct. 46) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the right-hand side of Resource B is increased by 30, and the right-hand side of Resource C is decreased by 10, then: A) the optimal solution remains the same. B) the optimal solution will change. C) the shadow prices are valid. D) the shadow prices may or may not be valid. E) None of the choices is correct. 9 Copyright © 2019 McGraw-Hill

47) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

What is the optimal objective function value for this problem? A) It cannot be determined from the given information. B) 1,200 C) 975 D) 8,250 E) 500

Allowable Decrease 1E+30 46 1E+30

49) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

What is the allowable range for the objective function coefficient for Activity 3? A) 150 ≤ A3 ≤ ∞ B) 0 ≤ A3 ≤ 650 C) 0 ≤ A3 ≤ 250 D) 400 ≤ A3 ≤ ∞ E) 300 ≤ A3 ≤ 500 50) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

What is the allowable range of the right-hand-side for Resource A? A) –∞ ≤ RHSA ≤ 60 B) 0 ≤ RHSA ≤ 110 C) –∞ ≤ RHSA ≤ 110 D) 110 ≤ RHSA ≤ 1600 E) 0 ≤ RHSA ≤ 160

Allowable Decrease 1E+30 46 1E+30

51) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

53) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

55) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

57) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the objective coefficients of Activity 2 and Activity 3 are both decreased by $100, then: A) the optimal solution remains the same. B) the optimal solution may or may not remain the same. C) the optimal solution will change. D) the shadow prices are valid. E) None of the choices is correct. 58) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

59) A parameter analysis report can be used to investigate the changes in how many data cells at a time? A) 1 B) 2 C) 3 D) All of the these. E) 1 or 2. 60) The allowable range for an objective function coefficient indicates A) The prices a firm is allowed to charge for its product. B) The largest error in estimating objective coefficients that will not affect the optimal solution. C) The amount of each resource available for use. D) The shadow price of each resource. E) The price a firm would be willing to obtain more of a resource. 61) To determine if an increase in an objective function coefficient will lead to a change in final values for decision variables, an analyst can do which of the following? I. Compare the increase in the objective function coefficient to the allowable decrease. II. Compare the increase in the objective function coefficient to the allowable increase. III. Rerun the optimization to see if the final values change. A) I only. B) II only. C) III only. D) I and III only. E) II and III only. 62) The Solver report that shows the allowable ranges for objective function coefficients, allowable ranges for constraint right-hand sides, and shadow prices is called the A) Range report. B) Sensitivity report. C) Parameter report. D) Solution report. E) Answer report. 63) Activity 1 has an objective function coefficient allowable increase of 30. Activity 2 has an objective function coefficient allowable increase of 60. If both activities objective function coefficient increases by 20, what will happen to the final values in the optimal solution? A) The optimal solution remains the same. B) The optimal solution may or may not remain the same. C) The optimal solution will change. D) The shadow prices are valid. E) None of the choices is correct.

64) Resource B has right-hand side allowable decrease of 50. Resource C has right-hand side allowable decrease of 100. If the right-hand side of Resource B decreases by 30 and the right-hand side of Resource C decreases by 40, then A) the original solution remains optimal. B) the problem must be resolved to find the optimal solution. C) the shadow prices remain valid. D) the shadow prices do not remain valid. E) None of the choices is correct. 65) Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase for the objective function coefficient for variable x? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) 3 B) 4.5 C) 9 D) 15 E) ∞ (infinity) 66) Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase in the right-hand side of the first constraint? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) 8 B) 10 C) 12 D) 15 E) ∞ (infinity)

67) Note: This question requires access to Solver. In the following linear programming problem, how much would the firm be willing to pay for an additional 5 units of Resource A? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 (Resource A) 5x + 2y ≤ 10 (Resource B) and x ≥ 0, y ≥ 0. A) It is impossible to determine. B) 7.50 C) 11.25 D) 15 E) 18.75 68) Note: This question requires access to Solver. In the following linear programming problem, how much would the firm be willing to pay for an additional 5 units of Resource B? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 (Resource A) 5x + 2y ≤ 10 (Resource B) and x ≥ 0, y ≥ 0. A) Nothing B) 11.25 C) 15 D) 18.75 E) It is impossible to determine. 69) In robust optimization, what is meant by the term "soft constraint"? A) A constraint that is not violated. B) A constraint that has a shadow price of zero. C) A constraint that can be violated slightly without serious repercussions. D) A constraint that can be violated dramatically without serious repercussions. E) A constraint that cannot be violated. 70) In robust optimization, what is meant by the term "hard constraint"? A) A constraint that is not violated. B) A constraint that has a shadow price of zero. C) A constraint that can be violated slightly without serious repercussions. D) A constraint that can be violated dramatically without serious repercussions. E) A constraint that cannot be violated. 71) One approach to robust optimization is to modify the original optimization problem by A) Assigning average values to each uncertain parameter. B) Assigning conservative values to each uncertain parameter. C) Assigning optimistic values to each uncertain parameter. D) Assigning random values to each uncertain parameter. E) Assigning precise values to each uncertain parameter. 18 Copyright © 2019 McGraw-Hill

72) When conducting robust optimization I. The right-hand side of each ≤ constraint should be replaced with the minimum value. II. The right-hand side of each ≤ constraint should be replaced with the maximum value. III. The right-hand side of each ≥ constraint should be replaced with the maximum value. A) I only B) II only C) III only D) I and III only E) II and III only 73) When conducting robust optimization I. Use the maximum value of each objective function coefficient for a maximization problem. II. Use the minimum value of each objective function coefficient for a maximization problem. III. Use the maximum value of each objective function coefficient for a minimization problem. A) I only B) II only C) III only D) I and III only E) II and III only 74) A chance constraint I. Replaces the right-hand side with the minimum value. II. Allows the objective function coefficients to be replaced with random numbers. III. Ensures that the chance constraint will never be violated. IV. Can be used to model a soft constraint which can be violated at times. A) I only B) II only C) III only D) IV only E) I and II only 75) Chance constraints are an available option in I. Graphical linear programming. II. The Solver tool included with Excel. III. Analytic Solver. A) I only B) II only C) III only D) II and III only E) I, II, and III

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 5 What-If Analysis for Linear Programming 1) An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem. Answer: TRUE Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Explain what is meant by what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) The purpose of a linear programming study is to help guide management's final decision by providing insights. Answer: TRUE Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Summarize the benefits of what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) It is usually quite easy to find the needed data for a linear programming study. Answer: FALSE Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Summarize the benefits of what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function, then management will want to take special care to narrow this estimate down. Answer: FALSE Difficulty: 2 Medium Topic: The Importance of What-if Analysis to Managers Learning Objective: Summarize the benefits of what-if analysis. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 1 Copyright © 2019 McGraw-Hill

5) Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem. Answer: TRUE Difficulty: 1 Easy Topic: The Effect of Single Changes in a Constraint Learning Objective: Predict how the value in the objective cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) When certain parameters of a model represent managerial policy decisions, what-if analysis provides information about what the impact would be of altering these policy decisions. Answer: TRUE Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Summarize the benefits of what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity. Answer: FALSE Difficulty: 1 Easy Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

8) The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate. Answer: TRUE Explanation: value may differ from its original estimate. Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 9) A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint. Answer: TRUE Difficulty: 1 Easy Topic: The Effect of Single Changes in a Constraint Learning Objective: Predict how the value in the objective cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) When maximizing profit in a linear programming problem, the allowable increase and allowable decrease columns in the sensitivity report make it possible to find the range over which the profitability does not change. Answer: FALSE Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

11) Changing the objective function coefficients may or may not change the optimal solution, but it will always change the value of the objective function. Answer: FALSE Difficulty: 1 Easy Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) Every change in the value of an objective function coefficient will lead to a changed optimal solution. Answer: FALSE Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 13) When a change in the value of an objective function coefficient remains within the allowable range, the optimal solution will also remain the same. Answer: TRUE Difficulty: 1 Easy Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) According to the 100% rule for simultaneous changes in objective function coefficients, if the sum of the percentage changes exceeds 100%, the optimal solution definitely will change. Answer: FALSE Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 4 Copyright © 2019 McGraw-Hill

15) Whenever proportional changes are made to all the unit profits in a problem, the optimal solution will remain the same. Answer: TRUE Difficulty: 1 Easy Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) The term "allowable range for the right-hand-side" refers to coefficients of the objective function. Answer: FALSE Difficulty: 1 Easy Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 17) If the change to a right-hand side is within the allowable range, the value of the shadow price remains valid. Answer: TRUE Difficulty: 1 Easy Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

18) If the change to a right-hand side is within the allowable range, the solution will remain the same. Answer: FALSE Difficulty: 1 Easy Topic: The Effect of Single Changes in a Constraint Learning Objective: Predict how the value in the objective cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) A shadow price tells how much a decision variable can be increased or decreased without changing the value of the solution. Answer: FALSE Difficulty: 1 Easy Topic: The Effect of Single Changes in a Constraint Learning Objective: Predict how the value in the objective cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) The allowable range gives ranges of values for the objective function coefficients within which the values of the decision variables are optimal. Answer: TRUE Difficulty: 1 Easy Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 21) When a change occurs in the right-hand side values of one of the constraints, a proportional change will occur in one of the coefficients of the objective function. Answer: FALSE Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 6 Copyright © 2019 McGraw-Hill

22) Managerial decisions regarding right-hand sides are often interrelated and so frequently are considered simultaneously. Answer: TRUE Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in the Constraints Learning Objective: Evaluate simultaneous changes in right-hand sides to determine whether the changes are small enough that this prediction must still be valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) If the sum of the percentage changes of the right-hand sides does not exceed 100%, then the solution will definitely remain optimal. Answer: FALSE Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in the Constraints Learning Objective: Evaluate simultaneous changes in right-hand sides to determine whether the changes are small enough that this prediction must still be valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 24) A parameter analysis report re-solves the problem for a range of values of a data cell. Answer: TRUE Difficulty: 1 Easy Topic: The Effect of Simultaneous Changes in the Constraints Learning Objective: Use Parameters with Analytic Solver to systematically investigate the effect of changing either one or two data cells to various other trial values. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 25) A parameter analysis report can only be used to investigate changes in a single data cell at a time. Answer: FALSE Difficulty: 1 Easy Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Use Parameters with Analytic Solver to systematically investigate the effect of changing either one or two data cells to various other trial values. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

26) A parameter analysis report can be used to easily investigate the changes in any number of data cells. Answer: FALSE Difficulty: 1 Easy Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Use Parameters with Analytic Solver to systematically investigate the effect of changing either one or two data cells to various other trial values. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) A shadow price reflects which of the following in a maximization problem? A) The marginal cost of adding additional resources. B) The marginal gain in the objective value realized by adding one unit of a resource. C) The marginal loss in the objective value realized by adding one unit of a resource. D) The marginal gain in the objective value realized by subtracting one unit of a resource. E) None of the choices is correct. Answer: B Difficulty: 1 Easy Topic: The Effect of Single Changes in a Constraint Learning Objective: Predict how the value in the objective cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) In linear programming, what-if analysis is associated with determining the effect of changing: I. objective function coefficients. II. right-hand side values of constraints. III. decision variable values. A) objective function coefficients and right-hand side values of constraints. B) right-hand side values of constraints and decision variable values. C) objective function coefficients, right-hand side values of constraints, and decision variable values. D) objective function coefficients and decision variable values. E) None of the choices is correct. Answer: A Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Explain what is meant by what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 8 Copyright © 2019 McGraw-Hill

29) What-if analysis can: I. be done graphically for problems with two decision variables. II. reduce a manager's confidence in the model that has been formulated. III. increase a manager's confidence in the model that has been formulated. A) I only. B) II only. C) III only. D) All of the these. E) I and III only. Answer: D Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Explain what is meant by what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) What-if analysis: A) may involve changes in the objective function coefficients. B) requires that only one parameter change while the rest are held fixed. C) may involve changes in the right-hand side values. D) All of the choices are correct. E) None of the choices is correct. Answer: D Difficulty: 2 Medium Topic: The Importance of What-if Analysis to Managers Learning Objective: Explain what is meant by what-if analysis. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

31) If a change is made in only one of the objective function coefficients: A) the slope of the objective function line always will change. B) the optimal solution always will change. C) one or more of the decision variables always will change. D) All of the choices are correct. E) None of the choices is correct. Answer: A Difficulty: 2 Medium Topic: The Importance of What-if Analysis to Managers Learning Objective: Enumerate the different kinds of changes in the model that can be considered by what-if analysis. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 32) If the right-hand side value of a constraint in a two variable linear programming problems is changed, then: A) the optimal measure of performance may change. B) a parallel shift must be made in the graph of that constraint. C) the optimal values for one or more of the decision variables may change. D) All of the choices are correct. E) None of the choices is correct. Answer: D Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 33) Which of the following are benefits of what-if analysis? A) It pinpoints the sensitive parameters of the model. B) It gives the new optimal solution if conditions change. C) It tells management what policy decisions to make. D) All of the choices are correct. E) None of the choices is correct. Answer: A Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Summarize the benefits of what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10 Copyright © 2019 McGraw-Hill

34) When even a small change in the value of a coefficient in the objective function can change the optimal solution, the coefficient is called: A) optimal. B) sensitive. C) out of the range. D) within the range. E) None of the choices is correct. Answer: B Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Summarize the benefits of what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) In a problem with 4 decision variables, the 100% rule indicates that each objective coefficient can be safely increased by what amount without invalidating the current optimal solution? A) 25%. B) 25% of the allowable increase of that coefficient. C) 100%. D) 25% of the range of optimality. E) It can't be determined from the information given. Answer: B Explanation: With 4 decision variables an increase of 25% of the allowable increase would result in a total change of 100% (4 × 25%), which does not violate the 100% rule. Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

36) variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

What is the optimal objective function value for this problem? A) It cannot be determined from the given information. B) $7.78 C) $240 D) $90 E) $330 Answer: E Difficulty: 2 Medium Topic: The Importance of What-if Analysis to Managers Learning Objective: Describe how the spreadsheet formulation of the problem can be used to perform any of these kinds of what-if analysis. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

37) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

What is the allowable range for the objective coefficient for Activity 2? A) −10 ≤ A2 ≤ 50 B) −44 ≤ A2 ≤ 16 C) −4 ≤ A2 ≤ 56 D) 30 ≤ A2 ≤ 90 E) 20 ≤ A2 ≤ 80 Answer: D Explanation: The objective coefficient for Activity 2 is 40. The allowable decrease is 10 and the allowable increase is 50. Therefore, the allowable range for this objective coefficient is (40 − 10) ≤ A2 ≤ (40 + 50) → 30 ≤ A2 ≤ 90 .(40-10)≤A2≤(40+50)→30≤A2≤90 (40-10)≤A2≤(40+50)→30≤A2≤90 Difficulty: 2 Medium Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

38) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

What is the allowable range for the right-hand-side for Resource C? A) 18 ≤ RHSc ≤ ∞ B) ∞ ≤ RHSc ≤ 62 C) −2 ≤RHSc ≤ ∞ D) − ∞ ≤ RHSc ≤ 40 E) 0 ≤ RHSc ≤ 22 Answer: A Explanation: The right-hand side for Resource C is 40. The allowable decrease is 22 and the allowable increase is ∞ (infinity). Therefore, the allowable range for this right-hand side is (40 − 22) ≤ RHSc ≤ (40 + ∞ ) → 18 ≤ RHSc ≤ ∞. Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

39) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the coefficient for Activity 1 in the objective function changes to $40, then the objective function value: A) will increase by $77.80. B) will increase by $23. C) will increase by $30. D) will remain the same. E) can only be discovered by resolving the problem. Answer: C Explanation: Increasing the objective function coefficient for Activity 1 to 40 is an increase of 10 (40 − 30 = 10). Since the allowable increase for this objective function coefficient is 23, this is within the allowable range and the optimal solution will not change. The final value for Activity 1 is 3, so increasing the objective function coefficient by 10 leads to an increase in the objective function of 30 {(40 − 30) × 3 = 30}. Difficulty: 3 Hard Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

40) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the coefficient for Activity 3 in the objective function changes to $30, then the objective function value: A) will increase by $70. B) is $0. C) will increase by $30. D) will remain the same. E) will increase by an unknown amount. Answer: E Explanation: Increasing the objective function coefficient for Activity 3 to 30 is an increase of 10 (30 − 20 = 10). Since the allowable increase for Activity 3 is 7, this change exceeds the allowable increase and the impact on the optimal solution cannot be determined without re-running the optimization. Difficulty: 3 Hard Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

41) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the coefficient of Activity 1 in the objective function changes to $10, then: A) the original solution remains optimal. B) the problem must be resolved to find the optimal solution. C) the shadow price is valid. D) the shadow price is not valid. E) None of the above. Answer: B Explanation: Decreasing the objective function coefficient for Activity 1 to 10 is a decrease of 20 (30 − 10 = 20). Since the allowable decrease for Activity 1 is 17, this change exceeds the allowable decrease and the impact on the optimal solution cannot be determined without re-running the optimization. Difficulty: 3 Hard Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

42) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the right-hand side of Resource A changes to 10, then the objective function value: A) will decrease by $12.50. B) will decrease by $125. C) will decrease by $77.80. D) will remain the same. E) can only be discovered by resolving the problem. Answer: C Explanation: Decreasing the constraint right-hand side for Resource A to 10 is a decrease of 10 (20 − 10 = 10). Since the allowable decrease for this constraint right-hand side is 12.5, this is within the allowable range and the shadow price still applies. A decrease of 10 in the constraint right-hand side leads to a decrease of 77.80 in the objective function—multiply the change in the constraint right-hand side by the shadow price {(20 − 10) × 7.78 = 77.80}. Difficulty: 3 Hard Topic: The Effect of Single Changes in a Constraint Learning Objective: Predict how the value in the objective cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

43) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the right-hand side of Resource B changes to 10, then the objective function value: A) will decrease by $120. B) will decrease by $60. C) will decrease by $20. D) will remain the same. E) can only be discovered by resolving the problem. Answer: E Explanation: Decreasing the constraint right-hand side for Resource B to 10 is a decrease of 20 (30 − 10 = 20). Since the allowable decrease for Resource B is 10, this change exceeds the allowable decrease and the impact on the optimal solution cannot be determined without re-running the optimization. Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

44) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 −7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the right-hand side of Resource B changes to 10, then: A) the original solution remains optimal. B) the problem must be resolved to find the optimal solution. C) the shadow price is valid. D) the shadow price is not valid. E) None of the choices is correct. Answer: D Explanation: Decreasing the constraint right-hand side for Resource B to 10 is a decrease of 20 (30 − 10 = 20). Since the allowable decrease for Resource B is 10, this change exceeds the allowable decrease and the impact on the optimal solution cannot be determined without re-running the optimization. Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

45) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

If the coefficients of Activity 1 and Activity 2 in the objective function are both increased by $10, then: A) the optimal solution remains the same. B) the optimal solution may or may not remain the same. C) the optimal solution will change. D) the shadow prices are valid. E) None of the choices is correct. Answer: A Explanation: Applying the 100% rule, the change in Activity 1 is 43.48% of the allowable increase

. The change in Activity 2 is 20% of the allowable increase

. The total change of 6.3.48% (43.48% + 20%) does not exceed 100%, so the optimal solution will not change. Difficulty: 3 Hard Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

46) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

. The change in

Resource C is 45.5% of the allowable decrease . The total change of 105.5% (60% + 45.5%) is greater than 100%, so the shadow prices may or may not remain valid. Difficulty: 2 Medium Topic: The Effect of Simultaneous Changes in the Constraints Learning Objective: Evaluate simultaneous changes in right-hand sides to determine whether the changes are small enough that this prediction must still be valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

47) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 3 0 30 23 17 6 0 40 50 10 0 –7 20 7 1E+30

Constraints Cell Name $E$2 Resource A $E$3 Resource B $E$4 Resource C

Final Shadow Value Price 20 7.78 30 6 18 0

Constraint Allowable Allowable R.H. Side Increase Decrease 20 10 12.5 30 50 10 40 1E+30 22

Which parameter is most sensitive to an increase in its value? A) The objective coefficient of Activity 1. B) The objective coefficient of Activity 2. C) The objective coefficient of Activity 3. D) All of the choices are correct. E) None of the choices is correct. Answer: C Explanation: The allowable increase for Activity 3 (7 according to the sensitivity report) is smaller than the allowable increases for both Activity 1 (allowable increase of 23) and Activity 2 (allowable increase of 50). Difficulty: 2 Medium Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

48) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

What is the optimal objective function value for this problem? A) It cannot be determined from the given information. B) 1,200 C) 975 D) 8,250 E) 500 Answer: D Explanation: The objective function value is calculated by multiplying the final value of each variable by the appropriate objective function coefficient. (425 × 0) + (300 × 27.5) + (400 × 0) = 8,250. Difficulty: 3 Hard Topic: The Importance of What-if Analysis to Managers Learning Objective: Enumerate the different kinds of changes in the model that can be considered by what-if analysis. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

49) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

What is the allowable range for the objective function coefficient for Activity 3? A) 150 ≤ A3 ≤ ∞ B) 0 ≤ A3 ≤ 650 C) 0 ≤ A3 ≤ 250 D) 400 ≤ A3 ≤ ∞ E) 300 ≤ A3 ≤ 500 Answer: A Explanation: The objective coefficient for Activity 3 is 400. The allowable decrease is 250 and the allowable increase is ∞ (infinity). Therefore, the allowable range for this objective coefficient is (400 − 250) ≤ A3 ≤ (40 + ∞) → 150 ≤ A3 ∞. Difficulty: 3 Hard Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

50) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

What is the allowable range of the right-hand-side for Resource A? A) –∞ ≤ RHSA ≤ 60 B) 0 ≤ RHSA ≤ 110 C) –∞ ≤ RHSA ≤ 110 D) 110 ≤ RHSA ≤ 1600 E) 0 ≤ RHSA ≤ 160 Answer: C Explanation: The right-hand side for Resource A is 60. The allowable decrease is ∞ (infinity) and the allowable increase is 50. Therefore, the allowable range for this right-hand side is (60 – ∞ ) ≤ RHSA ≤ (60 + 50 ) → −∞ ≤ RHSA ≤ 110. Difficulty: 3 Hard Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

51) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the coefficient for Activity 2 in the objective function changes to $400, then the objective function value: A) will increase by $7,500. B) will increase by $2,750. C) will increase by $100. D) will remain the same. E) can only be discovered by resolving the problem. Answer: B Explanation: Increasing the objective function coefficient for Activity 2 to 400 is an increase of 100 (400 − 300 = 100). Since the allowable increase for Activity 2 is 500, this change is within the range of optimality and the final values for the variables will not change. The new objective function value is calculated by multiplying the final value of each variable by the appropriate objective function coefficient. (425 × 0) + (400 × 27.5) + (400 × 0) = 11,000, which is an increase of 2,750 over the original objective function value of 8,250. Difficulty: 3 Hard Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

52) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the coefficient for Activity 1 in the objective function changes to $50, then the objective function value: A) will decrease by $450. B) is $0. C) will decrease by $2750. D) will remain the same. E) can only be discovered by resolving the problem. Answer: E Explanation: Decreasing the objective function coefficient for Activity 1 to 50 is a decrease of 450 (500 − 50 = 450). Since the allowable decrease for Activity 1 is 425, this change exceeds the allowable decrease and the impact on the optimal solution cannot be determined without re-running the optimization. Difficulty: 2 Medium Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

53) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the coefficient of Activity 2 in the objective function changes to $100, then: A) the original solution remains optimal. B) the problem must be resolved to find the optimal solution. C) the shadow price is valid. D) the shadow price is not valid. E) None of the choices is correct. Answer: A Explanation: Decreasing the objective function coefficient for Activity 2 to 100 is a decrease of 200 (300 − 100 = 200). Since the allowable decrease for Activity 2 is 300, this change is within the range of optimality and the final values for the variables will not change. Difficulty: 2 Medium Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

54) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the right-hand side of Resource B changes to 80, then the objective function value: A) will decrease by $750. B) will decrease by $1,500. C) will decrease by $2,250. D) will remain the same. E) can only be discovered by resolving the problem. Answer: C Explanation: Decreasing the constraint right-hand side for Resource B to 80 is a decrease of 30 (110 − 80 = 30). Since the allowable decrease for this constraint right-hand side is 46, this is within the allowable range and the optimal solution remains unchanged. A decrease of 20 in the constraint right-hand side leads to a decrease of 2,250 in the objective function—multiply the change in the constraint right-hand side by the shadow price {(110 − 80) × 75 = 2,250}. Difficulty: 3 Hard Topic: The Effect of Single Changes in a Constraint Learning Objective: Predict how the value in the objective cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

55) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the right-hand side of Resource C changes to 140, then the objective function value: A) will increase by $137.50. B) will increase by $57.50. C) will increase by $80. D) will remain the same. E) can only be discovered by resolving the problem. Answer: E Explanation: Increasing the constraint right-hand side for Resource C to 140 is an increase of 60 (140 − 80 = 60). Since the allowable increase for Resource C is 57.5, this change exceeds the allowable decrease and the impact on the optimal solution cannot be determined without re-running the optimization. Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

56) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the right-hand side of Resource C changes to 130, then: A) the original solution remains optimal. B) the problem must be resolved to find the optimal solution. C) the shadow price is valid. D) the shadow price is not valid. E) None of the choices is correct. Answer: C Explanation: Increasing the constraint right-hand side for Resource C to 130 is an increase of 50 (130 − 80 = 50). Since the allowable increase for Resource C is 57.5, this change is within the allowable limits and the shadow prices remain valid. Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

57) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the objective coefficients of Activity 2 and Activity 3 are both decreased by $100, then: A) the optimal solution remains the same. B) the optimal solution may or may not remain the same. C) the optimal solution will change. D) the shadow prices are valid. E) None of the choices is correct. Answer: A Explanation: Applying the 100% rule, the change in Activity 2 is 23.53% of the allowable decrease

. The change in Activity 3 is 40% of the allowable

decrease . The total change of 63.53% (23.53% + 40%) does not exceed 100%, so the optimal solution will not change. Difficulty: 3 Hard Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

58) Variable cells Cell Name $B$6 Activity 1 $C$6 Activity 2 $D$6 Activity 3

Final Value

Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 425 500 1E+30 425 27.5 0.0 300 500 300 0 250 400 1E+30 250

Constraints Cell Name $E$2 Benefit A $E$3 Benefit B $E$4 Benefit C

Final Shadow Value Price 110 0 110 75 137.5 0

Constraint Allowable R.H. Side Increase 60 50 110 1E+30 80 57.5

Allowable Decrease 1E+30 46 1E+30

If the right-hand side of Resource C is increased by 40, and the right-hand side of Resource B is decreased by 20, then: A) the optimal solution remains the same. B) the optimal solution will change. C) the shadow price is valid. D) the shadow price may or may not be not valid. E) None of the choices is correct. Answer: D Explanation: Both changes are within the allowable increase/decrease. Applying the 100% rule, the change in Resource B is 43.48% of the allowable decrease

. The change in

Resource C is 69.57% of the allowable increase . The total change of 113% (43.48% + 69.57%) is greater than 100%, so the shadow prices do not necessarily remain valid. Difficulty: 3 Hard Topic: The Effect of Simultaneous Changes in the Constraints Learning Objective: Evaluate simultaneous changes in right-hand sides to determine whether the changes are small enough that this prediction must still be valid. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

59) A parameter analysis report can be used to investigate the changes in how many data cells at a time? A) 1 B) 2 C) 3 D) All of the these. E) 1 or 2. Answer: E Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Use Parameters with Analytic Solver to systematically investigate the effect of changing either one or two data cells to various other trial values. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 60) The allowable range for an objective function coefficient indicates A) The prices a firm is allowed to charge for its product. B) The largest error in estimating objective coefficients that will not affect the optimal solution. C) The amount of each resource available for use. D) The shadow price of each resource. E) The price a firm would be willing to obtain more of a resource. Answer: B Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Enumerate the different kinds of changes in the model that can be considered by what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

61) To determine if an increase in an objective function coefficient will lead to a change in final values for decision variables, an analyst can do which of the following? I. Compare the increase in the objective function coefficient to the allowable decrease. II. Compare the increase in the objective function coefficient to the allowable increase. III. Rerun the optimization to see if the final values change. A) I only. B) II only. C) III only. D) I and III only. E) II and III only. Answer: E Difficulty: 2 Medium Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Find how much any single coefficient in the objective function can change without changing the optimal solution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 62) The Solver report that shows the allowable ranges for objective function coefficients, allowable ranges for constraint right-hand sides, and shadow prices is called the A) Range report. B) Sensitivity report. C) Parameter report. D) Solution report. E) Answer report. Answer: B Difficulty: 1 Easy Topic: The Importance of What-if Analysis to Managers Learning Objective: Describe how the spreadsheet formulation of the problem can be used to perform any of these kinds of what-if analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

63) Activity 1 has an objective function coefficient allowable increase of 30. Activity 2 has an objective function coefficient allowable increase of 60. If both activities objective function coefficient increases by 20, what will happen to the final values in the optimal solution? A) The optimal solution remains the same. B) The optimal solution may or may not remain the same. C) The optimal solution will change. D) The shadow prices are valid. E) None of the choices is correct. Answer: A Explanation: Applying the 100% rule, the change in Activity 1 is 66.67% of the allowable decrease

.The change in Activity 2 is 33.33% of the allowable decrease

. The total change of 100% (66.67% + 33.33%) does not exceed 100%, so the optimal solution will not change. Difficulty: 3 Hard Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 64) Resource B has right-hand side allowable decrease of 50. Resource C has right-hand side allowable decrease of 100. If the right-hand side of Resource B decreases by 30 and the right-hand side of Resource C decreases by 40, then A) the original solution remains optimal. B) the problem must be resolved to find the optimal solution. C) the shadow prices remain valid. D) the shadow prices do not remain valid. E) None of the choices is correct. Answer: C Explanation: Applying the 100% rule, the change in Resource B is 60% of the allowable decrease .The change in Resource C is 40% of the allowable decrease . The total change of 100% (60% + 40%) does not exceed 100%, so the shadow prices remain valid. Difficulty: 3 Hard Topic: The Effect of Simultaneous Changes in Objective Function Coefficients Learning Objective: Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 37 Copyright © 2019 McGraw-Hill

65) Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase for the objective function coefficient for variable x? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) 3 B) 4.5 C) 9 D) 15 E) ∞ (infinity) Answer: B Explanation: The sensitivity report (see below) shows that the allowable increase for variable x is 4.5. Variable cells Cell Name $B$3 x $C$4 y

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 0 –4.5 3 4.5 1E+30 3 0 15 1E+30 9

Constraints Cell Name $F$9 *y = $F$10 *y =

Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 12 3.75 12 8 12 6 0 10 1E+30 4

Difficulty: 2 Medium Topic: The Effect of Changes in One Objective Function Coefficient Learning Objective: Describe how the spreadsheet formulation of the problem can be used to perform any of these kinds of what-if analysis. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

66) Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase in the right-hand side of the first constraint? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) 8 B) 10 C) 12 D) 15 E) ∞ (infinity) Answer: A Explanation: The sensitivity report (see below) shows that the allowable increase for the right-hand side of constraint 1 is 8. Variable cells Cell Name $B$3 x $C$4 y

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 0 –4.5 3 4.5 1E+30 3 0 15 1E+30 9

Constraints Cell $F$9 $F$10

Name *y = *y =

Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 12 3.75 12 8 12 6 0 10 1E+30 4

Difficulty: 2 Medium Topic: The Effect of Single Changes in a Constraint Learning Objective: Describe how the spreadsheet formulation of the problem can be used to perform any of these kinds of what-if analysis. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 0 –4.5 3 4.5 1E+30 3 0 15 1E+30 9

Constraints Cell $F$9 $F$10

Name *y = *y =

Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 12 3.75 12 8 12 6 0 10 1E+30 4

Difficulty: 3 Hard Topic: The Effect of Single Changes in a Constraint Learning Objective: Describe how the spreadsheet formulation of the problem can be used to perform any of these kinds of what-if analysis. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

68) Note: This question requires access to Solver. In the following linear programming problem, how much would the firm be willing to pay for an additional 5 units of Resource B? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 (Resource A) 5x + 2y ≤ 10 (Resource B) and x ≥ 0, y ≥ 0. A) Nothing B) 11.25 C) 15 D) 18.75 E) It is impossible to determine. Answer: A Explanation: The sensitivity report (see below) shows that the allowable increase for the right-hand side of the second constraint is ∞ (infinity). Since the change is within this allowable increase, the shadow price remains valid. However, the shadow price of 0 indicates that the firm does not require any more of Resource B, so the firm will not be willing to pay anything to obtain 5 additional units. Variable cells Cell Name $B$3 x $C$4 y

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 0 –4.5 3 4.5 1E+30 3 0 15 1E+30 9

Constraints Cell $F$9 $F$10

Name *y = *y =

Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 12 3.75 12 8 12 6 0 10 1E+30 4

69) In robust optimization, what is meant by the term "soft constraint"? A) A constraint that is not violated. B) A constraint that has a shadow price of zero. C) A constraint that can be violated slightly without serious repercussions. D) A constraint that can be violated dramatically without serious repercussions. E) A constraint that cannot be violated. Answer: C Difficulty: 1 Easy Topic: Robust Optimization Learning Objective: Describe the goal of robust optimization and how it is implemented with independent parameters. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 70) In robust optimization, what is meant by the term "hard constraint"? A) A constraint that is not violated. B) A constraint that has a shadow price of zero. C) A constraint that can be violated slightly without serious repercussions. D) A constraint that can be violated dramatically without serious repercussions. E) A constraint that cannot be violated. Answer: E Difficulty: 1 Easy Topic: Robust Optimization Learning Objective: Describe the goal of robust optimization and how it is implemented with independent parameters. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 71) One approach to robust optimization is to modify the original optimization problem by A) Assigning average values to each uncertain parameter. B) Assigning conservative values to each uncertain parameter. C) Assigning optimistic values to each uncertain parameter. D) Assigning random values to each uncertain parameter. E) Assigning precise values to each uncertain parameter. Answer: B Difficulty: 2 Medium Topic: Robust Optimization Learning Objective: Describe the goal of robust optimization and how it is implemented with independent parameters. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 42 Copyright © 2019 McGraw-Hill

72) When conducting robust optimization I. The right-hand side of each ≤ constraint should be replaced with the minimum value. II. The right-hand side of each ≤ constraint should be replaced with the maximum value. III. The right-hand side of each ≥ constraint should be replaced with the maximum value. A) I only B) II only C) III only D) I and III only E) II and III only Answer: D Difficulty: 2 Medium Topic: Robust Optimization Learning Objective: Describe the goal of robust optimization and how it is implemented with independent parameters. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 73) When conducting robust optimization I. Use the maximum value of each objective function coefficient for a maximization problem. II. Use the minimum value of each objective function coefficient for a maximization problem. III. Use the maximum value of each objective function coefficient for a minimization problem. A) I only B) II only C) III only D) I and III only E) II and III only Answer: E Difficulty: 2 Medium Topic: Robust Optimization Learning Objective: Describe the goal of robust optimization and how it is implemented with independent parameters. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

74) A chance constraint I. Replaces the right-hand side with the minimum value. II. Allows the objective function coefficients to be replaced with random numbers. III. Ensures that the chance constraint will never be violated. IV. Can be used to model a soft constraint which can be violated at times. A) I only B) II only C) III only D) IV only E) I and II only Answer: D Difficulty: 2 Medium Topic: Chance Constraints With Analytic Solver Learning Objective: Use chance constraints to deal with constraints that actually can be violated a little bit. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 75) Chance constraints are an available option in I. Graphical linear programming. II. The Solver tool included with Excel. III. Analytic Solver. A) I only B) II only C) III only D) II and III only E) I, II, and III Answer: C Difficulty: 2 Medium Topic: Chance Constraints With Analytic Solver Learning Objective: Use chance constraints to deal with constraints that actually can be violated a little bit. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 6 Network Optimization Problems 1) Network representations can be used for financial planning. 2) A network representation is a very specific conceptual aid and is only used in special cases. 3) All network optimization problems actually are special types of linear programming problems. 4) Minimum cost flow problems are the special type of linear programming problem referred to as distribution-network problems. 5) A minimum cost flow problem may be summarized by drawing a network only after writing out the full formulation. 6) The model for any minimum cost flow problem is represented by a network with flow passing through it. 7) Each node in a minimum cost flow problem where the net amount of flow generated is a fixed positive number is a demand node. 8) Conservation of flow is achieved when the flow through a node is minimized. 9) Any node where the net amount of flow generated is fixed at zero is a transshipment node. 10) The amount of flow that is eventually sent through an arc is called the capacity of that arc. 11) In a minimum cost flow problem there can be only one supply node and only one demand node. 12) In a feasible minimum cost flow problem, the network has enough arcs with sufficient capacity to enable all the flow generated at the supply nodes to reach all the demand nodes. 13) In a minimum cost flow problem, the cost of the flow through each arc is proportional to the amount of that flow. 14) The objective of a minimum cost flow problem is to minimize the total cost of sending the available supply through the network even if all demand is not satisfied. 15) A minimum cost flow problem will have feasible solutions as long as there is a balance between the total supply from the supply nodes and the total demand at the demand nodes. 16) As long as all its supplies and demands have integer values, any minimum cost flow problem is guaranteed to have an optimal solution with integer values. 17) The network simplex method can be used to solve minimum cost flow problems with over a million arcs. 1 Copyright © 2019 McGraw-Hill

18) The network simplex method can aid managers in conducting what-if analysis. 19) A transportation problem is just a minimum cost flow problem without any transshipment nodes and without any capacity constraints on the arcs. 20) Any minimum cost flow problem where each arc can carry any desired amount of flow is a transshipment problem. 21) Maximum flow problems are concerned with maximizing the flow of goods through a distribution network. 22) In a true maximum flow problem there is only one source and one sink. 23) The source and sink of a maximum flow problem have conservation of flow. 24) In a maximum flow problem, flow is permitted in both directions and is represented by a pair of arcs pointing in opposite directions. 25) The objective of a maximum flow problem is to maximize the total profit generated by sending flow through a network. 26) The source and sink of a maximum flow problem are analogous to the supply nodes and demand nodes of a minimum cost flow problem. 27) In a maximum flow problem, the source and sink have fixed supplies and demands. 28) A maximum flow problem can be fit into the format of a minimum cost flow problem. 29) A network model showing the geographical layout of the problem is the usual way to represent a shortest path problem. 30) Shortest path problems are concerned with finding the shortest route through a network. 31) In a shortest path problem, the lines connecting the nodes are referred to as arcs. 32) In a shortest path problem there are no arcs permitted, only links. 33) A shortest path problem is required to have only a single destination. 34) When reformulating a shortest path problem as a minimum cost flow problem, each link should be replaced by a pair of arcs pointing in opposite directions. 35) Network representations can be used for the following problems: A) project planning. B) facilities location. C) financial planning. D) resource management. E) All of the choices are correct. 2 Copyright © 2019 McGraw-Hill

36) Which of the following will have negative net flow in a minimum cost flow problem? A) Supply nodes B) Transshipment nodes C) Demand nodes D) Arc capacities E) None of the choices is correct. 37) Which of the following is not an assumption of a minimum cost flow problem? A) At least one of the nodes is a supply node. B) There is an equal number of supply and demand nodes. C) Flow through an arc is only allowed in the direction indicated by the arrowhead. D) The cost of the flow through each arc is proportional to the amount of that flow. E) The objective is either to minimize the total cost or to maximize the total profit. 38) Which of the following is an example of a transshipment node? A) Storage facilities B) Processing facilities C) Short-term investment options D) Warehouses E) All of the choices are correct. 39) A minimum cost flow problem is a special type of: A) linear programming problem. B) transportation problem. C) spanning tree problem. D) transshipment problem. E) maximum flow problem. 40) Which of the following can be used to optimally solve minimum cost flow problems? I. The simplex method. II. The network simplex method. III. A greedy algorithm. A) I only. B) II only. C) III only. D) I and II only. E) All of these.

41) Which of the following problems are special types of minimum cost flow problems? I. Transportation problems. II. Assignment problems. III. Transshipment problems. IV. Shortest path problems. A) I and II only B) I, II, and III only C) IV only D) I, II, III, and IV E) None of the choices is correct. 42) For a minimum cost flow problem to have a feasible solution, which of the following must be true? A) There is the same number of supply nodes and demand nodes. B) There is only one supply node and one demand node. C) There is an equal amount of supply and demand. D) The supply and demand must be integers. E) The transshipment nodes must be able to absorb flow. 43) Which of the following is not an assumption of a maximum flow problem? A) All flow through the network originates at one node, called the source. B) If a node is not the source or the sink then it is a transshipment node. C) Flow can move toward the sink and away from the sink. D) The maximum amount of flow through an arc is given by the capacity of the arc. E) The objective is to maximize the total amount of flow from the source to the sink. 44) What is the objective of a maximum flow problem? A) Maximize the amount flowing through a network. B) Maximize the profit of the network. C) Maximize the routes being used. D) Maximize the amount produced at the origin. E) None of the choices is correct. 45) Which of the following could be the subject of a maximum flow problem? A) Products B) Oil C) Vehicles D) All of the choices are correct. E) None of the choices is correct. 46) Which of the following is not an assumption of a shortest path problem? A) The lines connecting certain pairs of nodes always allow travel in either direction. B) Associated with each link or arc is a nonnegative number called its length. C) A path through the network must be chosen going from the origin to the destination. D) The objective is to find a shortest path from the origin to the destination. E) None of the choices is correct. 4 Copyright © 2019 McGraw-Hill

47) Which of the following is an application of a shortest path problem? I. Minimize total distance traveled. II. Minimize total flow through a network. III. Minimize total cost of a sequence of activities. IV. Minimize total time of a sequence of activities A) I and II only B) I, II, and III only. C) IV only D) I, II, III, and IV E) I, III, and IV only. 48) In a shortest path problem, when "real travel" through a network can end at more than one node: I. An arc with length 0 is inserted. II. The problem cannot be solved. III. A dummy destination is needed. A) I only. B) II only. C) III only. D) I and II only. E) I and III only. 49) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

50) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

How many supply nodes are present in this problem? A) 1 B) 2 C) 3 D) 4 E) 5 51) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 How many demand nodes are present in this problem? A) 1 B) 2 C) 3 D) 4 E) 5

Customer 4 (75) $ 17 $ 20 $ 14

52) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

How many arcs will the network have? A) 3 B) 4 C) 7 D) 12 E) 15 53) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

54) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the minimum total cost to meet all customer requirements? A) $4,475 B) $4,500 C) $4,775 D) $4,950 E) $5,150 55) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

56) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

How many supply nodes are present in this problem? A) 1 B) 2 C) 3 D) 4 E) 5 57) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28 How many demand nodes are present in this problem? A) 1 B) 2 C) 3 D) 4 E) 5

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

58) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

How many arcs will the network have? A) 3 B) 4 C) 7 D) 12 E) 16 59) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

60) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the minimum total cost to meet all customer requirements? A) $8,750 B) $8,950 C) $9,000 D) $9,100 E) $10,050 61) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

62) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

Which nodes are the sink and source for this problem? A) Node A is the sink, Node I is the source. B) Node A is the sink, Node B is the source. C) Node B is the sink, Node I is the source. D) Node B is the source, Node I is the sink. E) Node A is the source, Node I is the sink. 63) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

How many transshipment nodes are present in this problem? A) 6 B) 7 C) 8 D) 1 E) 2

64) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

What is the capacity of the connection between nodes F and H? A) 3 TB/s B) 4 TB/s C) 10 TB/s D) 14 TB/s E) 15 TB/s 65) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

66) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the maximum amount of data that can be transmitted from node A to node I? A) 13 TB/s B) 23 TB/s C) 33 TB/s D) 43 TB/s E) 53 TB/s 67) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

68) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

Which nodes are the sink and source for this problem? A) Node A is the sink, Node I is the source. B) Node A is the sink, Node B is the source. C) Node B is the sink, Node I is the source. D) Node B is the source, Node I is the sink. E) Node A is the source, Node I is the sink. 69) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

70) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

What is the capacity of the connection between nodes B and E? A) 9 packages/day B) 11 packages/day C) 16 packages/day D) 21 packages/day E) 26 packages/day 71) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

72) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

73) The figure below shows the nodes (A – I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the maximum amount of data that can be transmitted from node A to node I? A) 13 packages/day. B) 23 packages/day. C) 34 packages/day. D) 43 packages/day. E) 53 packages/day. 74) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

75) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

Which of the following paths would be infeasible? A) A-B-D-G-J-L-M B) A-B-E-G-J-L-M C) A-C-F-H-K-M D) A-B-D-G-I-M E) A-C-F-I-G-J-L-M 76) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

77) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. Which of the following nodes are not visited? A) A B) B C) C D) A and B E) A and C

78) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

79) The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the quickest option to travel from city A to city J.

80) The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the quickest option to travel from city A to city J.

81) The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the quickest option to travel from city A to city J.

Which of the following paths would be infeasible? A) A-B-C-E-G-I-J B) A-B-C-F-E-G-I-J C) A-B-D-G-I-J D) A-C-F-J E) A-C-F-E-G-I-J

82) The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the quickest option to travel from city A to city J.

What is the time to travel between nodes F and J? A) 120 B) 140 C) 160 D) 180 E) 200

83) The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the quickest option to travel from city A to city J.

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. Which of the following nodes are not visited? A) B B) E C) H D) B and E E) E and H

84) The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the quickest option to travel from city A to city J.

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 6 Network Optimization Problems 1) Network representations can be used for financial planning. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Identify some areas of application for these types of problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) A network representation is a very specific conceptual aid and is only used in special cases. Answer: FALSE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) All network optimization problems actually are special types of linear programming problems. Answer: FALSE Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) Minimum cost flow problems are the special type of linear programming problem referred to as distribution-network problems. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 1 Copyright © 2019 McGraw-Hill

5) A minimum cost flow problem may be summarized by drawing a network only after writing out the full formulation. Answer: FALSE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) The model for any minimum cost flow problem is represented by a network with flow passing through it. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) Each node in a minimum cost flow problem where the net amount of flow generated is a fixed positive number is a demand node. Answer: FALSE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) Conservation of flow is achieved when the flow through a node is minimized. Answer: FALSE Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 2 Copyright © 2019 McGraw-Hill

9) Any node where the net amount of flow generated is fixed at zero is a transshipment node. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) The amount of flow that is eventually sent through an arc is called the capacity of that arc. Answer: FALSE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) In a minimum cost flow problem there can be only one supply node and only one demand node. Answer: FALSE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) In a feasible minimum cost flow problem, the network has enough arcs with sufficient capacity to enable all the flow generated at the supply nodes to reach all the demand nodes. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) In a minimum cost flow problem, the cost of the flow through each arc is proportional to the amount of that flow. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) The objective of a minimum cost flow problem is to minimize the total cost of sending the available supply through the network even if all demand is not satisfied. Answer: FALSE Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) A minimum cost flow problem will have feasible solutions as long as there is a balance between the total supply from the supply nodes and the total demand at the demand nodes. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) As long as all its supplies and demands have integer values, any minimum cost flow problem is guaranteed to have an optimal solution with integer values. Answer: TRUE Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 4 Copyright © 2019 McGraw-Hill

17) The network simplex method can be used to solve minimum cost flow problems with over a million arcs. Answer: TRUE Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Identify some areas of application for these types of problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) The network simplex method can aid managers in conducting what-if analysis. Answer: TRUE Difficulty: 2 Medium Topic: A Case Study: The BMZ Co. Maximum Flow Problem Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) A transportation problem is just a minimum cost flow problem without any transshipment nodes and without any capacity constraints on the arcs. Answer: TRUE Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) Any minimum cost flow problem where each arc can carry any desired amount of flow is a transshipment problem. Answer: TRUE Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

21) Maximum flow problems are concerned with maximizing the flow of goods through a distribution network. Answer: TRUE Difficulty: 1 Easy Topic: Maximum Flow Problems Learning Objective: Identify some areas of application for these types of problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) In a true maximum flow problem there is only one source and one sink. Answer: TRUE Difficulty: 1 Easy Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) The source and sink of a maximum flow problem have conservation of flow. Answer: FALSE Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 24) In a maximum flow problem, flow is permitted in both directions and is represented by a pair of arcs pointing in opposite directions. Answer: FALSE Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

25) The objective of a maximum flow problem is to maximize the total profit generated by sending flow through a network. Answer: FALSE Difficulty: 1 Easy Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) The source and sink of a maximum flow problem are analogous to the supply nodes and demand nodes of a minimum cost flow problem. Answer: TRUE Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) In a maximum flow problem, the source and sink have fixed supplies and demands. Answer: FALSE Difficulty: 1 Easy Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) A maximum flow problem can be fit into the format of a minimum cost flow problem. Answer: TRUE Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

29) A network model showing the geographical layout of the problem is the usual way to represent a shortest path problem. Answer: FALSE Difficulty: 1 Easy Topic: Shortest Path Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) Shortest path problems are concerned with finding the shortest route through a network. Answer: TRUE Difficulty: 1 Easy Topic: Shortest Path Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) In a shortest path problem, the lines connecting the nodes are referred to as arcs. Answer: FALSE Difficulty: 1 Easy Topic: Shortest Path Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 32) In a shortest path problem there are no arcs permitted, only links. Answer: FALSE Difficulty: 1 Easy Topic: Shortest Path Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

33) A shortest path problem is required to have only a single destination. Answer: TRUE Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 34) When reformulating a shortest path problem as a minimum cost flow problem, each link should be replaced by a pair of arcs pointing in opposite directions. Answer: TRUE Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) Network representations can be used for the following problems: A) project planning. B) facilities location. C) financial planning. D) resource management. E) All of the choices are correct. Answer: E Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Identify some areas of application for these types of problems. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

36) Which of the following will have negative net flow in a minimum cost flow problem? A) Supply nodes B) Transshipment nodes C) Demand nodes D) Arc capacities E) None of the choices is correct. Answer: C Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 37) Which of the following is not an assumption of a minimum cost flow problem? A) At least one of the nodes is a supply node. B) There is an equal number of supply and demand nodes. C) Flow through an arc is only allowed in the direction indicated by the arrowhead. D) The cost of the flow through each arc is proportional to the amount of that flow. E) The objective is either to minimize the total cost or to maximize the total profit. Answer: B Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) Which of the following is an example of a transshipment node? A) Storage facilities B) Processing facilities C) Short-term investment options D) Warehouses E) All of the choices are correct. Answer: E Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Identify several categories of network optimization problems that are special types of minimum-cost flow problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 10 Copyright © 2019 McGraw-Hill

39) A minimum cost flow problem is a special type of: A) linear programming problem. B) transportation problem. C) spanning tree problem. D) transshipment problem. E) maximum flow problem. Answer: A Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 40) Which of the following can be used to optimally solve minimum cost flow problems? I. The simplex method. II. The network simplex method. III. A greedy algorithm. A) I only. B) II only. C) III only. D) I and II only. E) All of these. Answer: D Difficulty: 1 Easy Topic: Minimum-Cost Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

43) Which of the following is not an assumption of a maximum flow problem? A) All flow through the network originates at one node, called the source. B) If a node is not the source or the sink then it is a transshipment node. C) Flow can move toward the sink and away from the sink. D) The maximum amount of flow through an arc is given by the capacity of the arc. E) The objective is to maximize the total amount of flow from the source to the sink. Answer: C Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 44) What is the objective of a maximum flow problem? A) Maximize the amount flowing through a network. B) Maximize the profit of the network. C) Maximize the routes being used. D) Maximize the amount produced at the origin. E) None of the choices is correct. Answer: A Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Describe the characteristics of minimum-cost flow problems, maximum flow problems, and shortest path problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 45) Which of the following could be the subject of a maximum flow problem? A) Products B) Oil C) Vehicles D) All of the choices are correct. E) None of the choices is correct. Answer: D Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Identify some areas of application for these types of problems. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

46) Which of the following is not an assumption of a shortest path problem? A) The lines connecting certain pairs of nodes always allow travel in either direction. B) Associated with each link or arc is a nonnegative number called its length. C) A path through the network must be chosen going from the origin to the destination. D) The objective is to find a shortest path from the origin to the destination. E) None of the choices is correct. Answer: A Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate network models for various types of network optimization problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 47) Which of the following is an application of a shortest path problem? I. Minimize total distance traveled. II. Minimize total flow through a network. III. Minimize total cost of a sequence of activities. IV. Minimize total time of a sequence of activities A) I and II only B) I, II, and III only. C) IV only D) I, II, III, and IV E) I, III, and IV only. Answer: E Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Identify some areas of application for these types of problems. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

48) In a shortest path problem, when "real travel" through a network can end at more than one node: I. An arc with length 0 is inserted. II. The problem cannot be solved. III. A dummy destination is needed. A) I only. B) II only. C) III only. D) I and II only. E) I and III only. Answer: E Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 49) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

Which type of network optimization problem is used to solve this problem? A) Maximum-Cost Flow problem B) Minimum-Cost Flow problem C) Maximum Flow Problem D) Minimum Flow Problem E) Shortest Path Problem Answer: B Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 15 Copyright © 2019 McGraw-Hill

Customer 4 (75) $ 17 $ 20 $ 14

How many supply nodes are present in this problem? A) 1 B) 2 C) 3 D) 4 E) 5 Answer: C Explanation: Each of the three factories is a supply node. Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

51) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

How many demand nodes are present in this problem? A) 1 B) 2 C) 3 D) 4 E) 5 Answer: D Explanation: Each of the four customers is a demand node. Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

Customer 4 (75) $ 17 $ 20 $ 14

How many arcs will the network have? A) 3 B) 4 C) 7 D) 12 E) 15 Answer: D Explanation: With 3 supply nodes and 4 demand nodes, there will be 12 {3x4} arcs in the network. Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

53) A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (25) Customer 2 (50) (125) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25

Customer 4 (75) $ 17 $ 20 $ 14

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the optimal quantity to ship from Factory A to Customer 2? A) 25 units B) 50 units C) 75 units D) 100 units E) 125 units Answer: B Explanation: Using Solver, the optimal quantity to ship from source A to destination 2 is 50 units. The problem formulation is (where i represents the destinations and j represents the source) (capacity constraint for each source) (demand constraint for each destination) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Customer 4 (75) $ 17 $ 20 $ 14

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the minimum total cost to meet all customer requirements? A) $4,475 B) $4,500 C) $4,775 D) $4,950 E) $5,150 Answer: A Explanation: Using Solver, minimum cost to meet all customer demand is $4,475. The problem formulation is (where i represents the destinations and j represents the source) (capacity constraint for each source) (demand constraint for each destination) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

55) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

How many supply nodes are present in this problem? A) 1 B) 2 C) 3 D) 4 E) 5 Answer: D Explanation: Each of the four factories is a supply node. Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

57) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

How many arcs will the network have? A) 3 B) 4 C) 7 D) 12 E) 16 Answer: E Explanation: With 4 supply nodes and 4 demand nodes, there will be 16 {4 × 4} arcs in the network. Difficulty: 2 Medium Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

59) A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Customer 3 Factory (capacity) Customer 1 (125)Customer 2 (150) (175) A (100) $ 15 $ 10 $ 20 B (75) $ 20 $ 12 $ 19 C (100) $ 22 $ 20 $ 25 D (250) $ 21 $ 15 $ 28

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the optimal quantity to ship from Factory B to Customer 3? A) 25 units B) 50 units C) 75 units D) 100 units E) 125 units Answer: C Explanation: Using Solver, the optimal quantity to ship from source B to destination 3 is 75 units. The problem formulation is (where i represents the destinations and j represents the source) (capacity constraint for each source) (demand constraint for each destination) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Customer 4 (75) $ 17 $ 20 $ 14 $ 12

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the minimum total cost to meet all customer requirements? A) $8,750 B) $8,950 C) $9,000 D) $9,100 E) $10,050 Answer: D Explanation: Using Solver, minimum cost to meet all customer demand is $9,100. The problem formulation is (where i represents the destinations and j represents the source) (capacity constraint for each source) (demand constraint for each destination) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

61) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

Which type of network optimization problem is used to solve this problem? A) Maximum-Cost Flow problem B) Minimum-Cost Flow problem C) Maximum Flow Problem D) Minimum Flow Problem E) Shortest Path Problem Answer: C Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

62) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

Which nodes are the sink and source for this problem? A) Node A is the sink, Node I is the source. B) Node A is the sink, Node B is the source. C) Node B is the sink, Node I is the source. D) Node B is the source, Node I is the sink. E) Node A is the source, Node I is the sink. Answer: E Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

63) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

How many transshipment nodes are present in this problem? A) 6 B) 7 C) 8 D) 1 E) 2 Answer: B Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

64) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

What is the capacity of the connection between nodes F and H? A) 3 TB/s B) 4 TB/s C) 10 TB/s D) 14 TB/s E) 15 TB/s Answer: D Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

65) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. At maximum capacity, what will be the data flow between nodes F and H? A) 3 TB/s B) 4 TB/s C) 10 TB/s D) 14 TB/s E) 15 TB/s Answer: C Explanation: Using Solver, the optimal quantity to ship from node F to node H is 10 TB/s. The problem formulation is (capacity constraint for each arc) (flow into node equals flow out of node) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

66) The figure below shows the nodes (A–I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I.

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the maximum amount of data that can be transmitted from node A to node I? A) 13 TB/s B) 23 TB/s C) 33 TB/s D) 43 TB/s E) 53 TB/s Answer: C Explanation: Using Solver, the optimal quantity to ship from node A to node I is 33 TB/s. The problem formulation is (capacity constraint for each arc) (flow into node equals flow out of node) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

67) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

Which type of network optimization problem is used to solve this problem? A) Maximum-Cost Flow problem B) Minimum-Cost Flow problem C) Maximum Flow Problem D) Minimum Flow Problem E) Shortest Path Problem Answer: C Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which nodes are the sink and source for this problem? A) Node A is the sink, Node I is the source. B) Node A is the sink, Node B is the source. C) Node B is the sink, Node I is the source. D) Node B is the source, Node I is the sink. E) Node A is the source, Node I is the sink. Answer: E Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

69) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

What is the capacity of the connection between nodes B and E? A) 9 packages/day B) 11 packages/day C) 16 packages/day D) 21 packages/day E) 26 packages/day Answer: D Difficulty: 2 Medium Topic: Maximum Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

71) The figure below shows the nodes (A–I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I.

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. At maximum capacity, what will be the flow between nodes B and E? A) 9 packages/day B) 11 packages/day C) 16 packages/day D) 21 packages/day E) 26 packages/day Answer: A Explanation: Using Solver, the optimal quantity to ship from node B to node E is 9 packages/day. The problem formulation is (capacity constraint for each arc) (flow into node equals flow out of node) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Which type of network optimization problem is used to solve this problem? A) Maximum-Cost Flow problem B) Average-Cost Flow problem C) Maximum Flow Problem D) Minimum Flow Problem E) Shortest Path Problem Answer: E Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the maximum amount of data that can be transmitted from node A to node I? A) 13 packages/day. B) 23 packages/day. C) 34 packages/day. D) 43 packages/day. E) 53 packages/day. Answer: C Explanation: Using Solver, the maximum quantity to ship from node A to node I is 34 packages/day. The problem formulation is (capacity constraint for each arc) (flow into node equals flow out of node) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

74) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

Which nodes are the origin and destination for this problem? A) Node A is the origin, Node I is the destination. B) Node A is the origin, Node M is the destination. C) Node B is the origin, Node I is the destination. D) Node B is the destination, Node I is the origin. E) Node A is the destination, Node I is the origin. Answer: B Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the following paths would be infeasible? A) A-B-D-G-J-L-M B) A-B-E-G-J-L-M C) A-C-F-H-K-M D) A-B-D-G-I-M E) A-C-F-I-G-J-L-M Answer: C Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

76) The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M.

What is the cost of the connection between nodes K and I? A) 9 B) 11 C) 16 D) 21 E) 26 Answer: B Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. Which of the following nodes are not visited? A) A B) B C) C D) A and B E) A and C Answer: E Explanation: Using Solver, the optimal solution includes visiting nodes A and C, but not node B. The problem formulation is: (where i and j are the start and end of each arc)

(traveler must leave node A exactly once) (traveler must arrive at node M exactly once) (flow into node equals flow out of node for all nodes except nodes A and M) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation 43 Copyright © 2019 McGraw-Hill

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the minimum cost for the traveler to move from node A to node M? A) $76 B) $86 C) $96 D) $106 E) $116 Answer: D Explanation: Using Solver, the minimum cost is $106. The problem formulation is: (where i and j are the start and end of each arc)

(traveler must leave node A exactly once) (traveler must arrive at node M exactly once) (flow into node equals flow out of node for all nodes except nodes A and M) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation 44 Copyright © 2019 McGraw-Hill

Which nodes are the origin and destination for this problem? A) Node A is the origin, Node J is the destination. B) Node A is the origin, Node M is the destination. C) Node B is the origin, Node I is the destination. D) Node B is the destination, Node I is the origin. E) Node A is the destination, Node I is the origin. Answer: A Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the following paths would be infeasible? A) A-B-C-E-G-I-J B) A-B-C-F-E-G-I-J C) A-B-D-G-I-J D) A-C-F-J E) A-C-F-E-G-I-J Answer: A Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

What is the time to travel between nodes F and J? A) 120 B) 140 C) 160 D) 180 E) 200 Answer: A Difficulty: 2 Medium Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. Which of the following nodes are not visited? A) B B) E C) H D) B and E E) E and H Answer: D Explanation: Using Solver, the optimal solution includes visiting node H, but not nodes B and E. The problem formulation is: (where i and j are the start and end of each arc)

(traveler must leave node A exactly once) (traveler must arrive at node J exactly once) (flow into node equals flow out of node for all nodes except nodes A and J) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Shortest Path Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation 49 Copyright © 2019 McGraw-Hill

Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the minimum cost for the traveler to move from node A to node J? A) 305 minutes B) 310 minutes C) 315 minutes D) 320 minutes E) 325 minutes Answer: A Explanation: Using Solver, the minimum time is 305 minutes. The problem formulation is: (where i and j are the start and end of each arc)

(traveler must leave node A exactly once) (traveler must arrive at node J exactly once) (flow into node equals flow out of node for all nodes except nodes A and J) (quantity shipped must be non-negative) Difficulty: 3 Hard Topic: Minimum-Cost Flow Problems Learning Objective: Formulate and solve a spreadsheet model for a minimum-cost flow problem, a maximum flow problem, or a shortest path problem from a description of the problem. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation 50 Copyright © 2019 McGraw-Hill

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 7 Using Binary Integer Programming to Deal with Yes-or-No Decisions 1) Binary integer programming problems are those where all the decision variables restricted to integer values are further restricted to be binary variables. 2) Binary variables are variables whose only possible values are 0 or 1. 3) Variables whose only possible values are 0 and 1 are called integer variables. 4) A problems where all the variables are binary variables is called a pure BIP problem. 5) Binary variables are best suited to be the decision variables when dealing with yes-or-no decisions. 6) A BIP problem considers one yes-or-no decision at a time with the objective of choosing the best alternative. 7) The algorithms available for solving BIP problems are much more efficient than those for linear programming which is one of the advantages of formulating problems this way. 8) If choosing one alternative from a group excludes choosing all of the others then these alternatives are called mutually exclusive. 9) The constraint x1 + x2 + x3 ≤ 3 in a BIP represents mutually exclusive alternatives. 10) It is possible to have a constraint in a BIP that excludes the possibility of choosing none of the alternatives available. 11) A yes-or-no decision is a mutually exclusive decision if it can be yes only if a certain other yes-or-no decision is yes. 12) The constraint x1 ≤ x2 in a BIP problem means that alternative 2 cannot be selected unless alternative 1 is also selected. 13) BIP can be used in capital budgeting decisions to determine whether to invest a certain amount. 14) BIP can be used to determine the timing of activities. 15) An auxiliary binary variable is an additional binary variable that is introduced into a model to represent additional yes-or-no decisions. 16) A linear programming formulation is not valid for a product mix problem when there are setup costs for initiating production.

17) The Excel sensitivity report can be used to perform sensitivity analysis for integer programming problems. 18) A parameter analysis report can be used to perform sensitivity analysis for integer programming problems. 19) To model a situation where a setup cost will be charged if a certain product is produced, the best approach is to include and Excel "IF" function. 20) In a site selection problem, a common goal is to identify the set of locations that provides adequate service at the minimum cost. 21) In a crew scheduling problem there is no need for a set covering constraint. 22) If activities A and B are mutually exclusive, the constraint xA ≤ xB will enforce this relationship in a linear program. 23) If a firm wishes to choose at most 2 of 4 possible activities (A, B, C and D), the constraint xA + xB + xC + xD ≥ 2 will enforce this relationship in a linear program. 24) If a firm wishes to choose at least 2 of 4 possible activities (A, B, C and D), the constraint xA + xB + xC + xD ≥ 2 will enforce this relationship in a linear program. 25) When binary variables are used in a linear program, the Solver Sensitivity Report is not available. 26) Binary integer programming problems can answer which types of questions? A) Should a project be undertaken? B) Should an investment be made? C) Should a plant be located at a particular location? D) All of the choices are correct. E) None of the choices is correct. 27) Binary variables can have the following values: A) 0 only. B) 1 only. C) any integer value less than 1. D) 0 and 1 only. E) any integer value greater than 1. 28) Binary integer programming can be used for: A) capital budgeting. B) site selection. C) scheduling asset divestitures. D) assignments of routes. E) All of the choices are correct. 2 Copyright © 2019 McGraw-Hill

29) In a BIP problem with 2 mutually exclusive alternatives, x1 and x2, the following constraint needs to be added to the formulation: A) x1 + x2 ≤ 1. B) x1 + x2 ≥ 1. C) x1 – x2 ≤ 1. D) x1 – x2 = 1. E) None of the choices is correct. 30) In a BIP problem with 2 mutually exclusive alternatives, x1 and x2, the following constraint needs to be added to the formulation if one alternative must be chosen: A) x1 + x2 ≤ 1. B) x1 + x2 = 1. C) x1 – x2 ≤ 1. D) x1– x2 = 1. E) None of the choices is correct. 31) In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If project A can be undertaken only if project B is also undertaken then the following constraint needs to be added to the formulation: A) A + B ≤ 1. B) A + B = 1. C) A ≤ B. D) B ≤ A. E) None of the choices is correct. 32) In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If there are two projects under consideration, A and B, and either both projects will be undertaken or no project will be undertaken, then the following constraint needs to be added to the formulation: A) A ≤ B. B) A + B ≤ 2. C) A ≥ B. D) A = B. E) None of the choices is correct. 33) In a BIP problem with 3 mutually exclusive alternatives, x1, x2, and x3, the following constraint needs to be added to the formulation: A) x1 + x2 + x3 ≤ 1. B) x1 + x2 + x3 = 1. C) x1 – x2 – x3 ≤ 1. D) x1 – x2 – x3 = 1. E) None of the choices is correct.

34) In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If there are 4 projects under consideration (A, B, C, and D) and at most 2 can be chosen then the following constraint needs to be added to the formulation: A) A + B + C + D ≤ 1. B) A + B + C + D ≤ 2. C) A + B + C + D ≤ 4. D) A + B + C + D = 2. E) None of the choices is correct. 35) Which of the following techniques or tools can be used to perform sensitivity analysis for an integer programming problem? I. The sensitivity report. II. Trial-and-error. III. A parameter analysis report. A) I only B) II only C) III only D) I and II only E) All of the choices are correct. 36) A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Which of the constraints enforces a mutually exclusive relationship? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5

37) A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Which of the constraints enforces a contingent relationship? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 38) A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Which of the constraints ensures that at least two of the potential sites will be selected? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5

39) A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Which constraint ensures that the firm will not spend more capital than it has available (assume that each potential location has a different cost)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 40) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Set up the problem in Excel and find the optimal solution. Which locations are selected? A) Location 1 B) Location 2 C) Location 4 D) Locations 2 and 4 E) Locations 1 and 3

41) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Set up the problem in Excel and find the optimal solution. What is the expected net present value of the optimal solution? A) 20 B) 30 C) 35 D) 40 E) 45 42) A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Which of the constraints enforces a mutually exclusive relationship? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5

43) A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Which of the constraints enforces a contingent relationship? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 44) A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Which of the constraints ensures that at least two of the potential projects will be selected? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5

45) A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Which constraint ensures that the firm will not spend more capital than it has available (assume that each potential project has a different cost)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 46) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Set up the problem in Excel and find the optimal solution. Which projects are selected? A) Project 1 B) Project 2 C) Project 4 D) Projects 2 and 3 E) Projects 1 and 3

47) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Set up the problem in Excel and find the optimal solution. What is the expected net present value of the optimal solution? A) 210 B) 220 C) 235 D) 310 E) 435

48) A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model: Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8 s.t.x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint} x1 + x2 + x3 ≥ 1 {Neighborhood B constraint} x5 + x6 + x8 ≥ 1 {Neighborhood C constraint} x1 + x4 + x7 ≥ 1 {Neighborhood D constraint} x2 + x3 + x7 ≥ 1 {Neighborhood E constraint} x3 + x4 + x8 ≥ 1 {Neighborhood F constraint} x2 + x5 + x7 ≥ 1 {Neighborhood G constraint} x1 + x4 + x6 ≥ 1 {Neighborhood H constraint} x1 + x6 + x8 ≥ 1 {Neighborhood I constraint} x1 + x2 + x7 ≥ 1 {Neighborhood J constraint}

49) A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model: Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint} x1 + x2 + x3 ≥ 1 {Neighborhood B constraint} x5 + x6 + x8 ≥ 1 {Neighborhood C constraint} x1 + x4 + x7 ≥ 1 {Neighborhood D constraint} x2 + x3 + x7 ≥ 1 {Neighborhood E constraint} x3 + x4 + x8 ≥ 1 {Neighborhood F constraint} x2 + x5 + x7 ≥ 1 {Neighborhood G constraint} x1 + x4 + x6 ≥ 1 {Neighborhood H constraint} x1 + x6 + x8 ≥ 1 {Neighborhood I constraint} x1 + x2 + x7 ≥ 1 {Neighborhood J constraint}

Which of the locations is the most expensive? A) Location 1. B) Location 2. C) Location 3. D) Location 4. E) Location 5.

50) A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model: Min 100x1 + 120x2 + 90x3 + 135x4 +75x 5 + 85x6 + 110x7 + 135x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint} x1 + x2 + x3 ≥ 1 {Neighborhood B constraint} x5 + x6 + x8 ≥ 1 {Neighborhood C constraint} x1 + x4 + x7 ≥ 1 {Neighborhood D constraint} x2 + x3 + x7 ≥ 1 {Neighborhood E constraint} x3 + x4 + x8 ≥ 1 {Neighborhood F constraint} x2 + x5 + x7 ≥ 1 {Neighborhood G constraint} x1 + x4 + x6 ≥ 1 {Neighborhood H constraint} x1 + x6 + x8 ≥ 1 {Neighborhood I constraint} x1 + x2 + x7 ≥ 1 {Neighborhood J constraint}

51) A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model: Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint} x1 + x2 + x3 ≥ 1 {Neighborhood B constraint} x5 + x6 + x8 ≥ 1 {Neighborhood C constraint} x1 + x4 + x7 ≥ 1 {Neighborhood D constraint} x2 + x3 + x7 ≥ 1 {Neighborhood E constraint} x3 + x4 + x8 ≥ 1 {Neighborhood F constraint} x2 + x5 + x7 ≥ 1 {Neighborhood G constraint} x1 + x4 + x6 ≥ 1 {Neighborhood H constraint} x1 + x6 + x8 ≥ 1 {Neighborhood I constraint} x1 + x2 + x7 ≥ 1 {Neighborhood J constraint}

Which of the locations is NOT within 15 minutes of neighborhood A? A) Location 1 B) Location 2 C) Location 5 D) Location 6 E) Location 7

52) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model: Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint} x1 + x2 + x3 ≥ 1 {Neighborhood B constraint} x5 + x6 + x8 ≥ 1 {Neighborhood C constraint} x1 + x4 + x7 ≥ 1 {Neighborhood D constraint} x2 + x3 + x7 ≥ 1 {Neighborhood E constraint} x3 + x4 + x8 ≥ 1 {Neighborhood F constraint} x2 + x5 + x7 ≥ 1 {Neighborhood G constraint} x1 + x4 + x6 ≥ 1 {Neighborhood H constraint} x1 + x6 + x8 ≥ 1 {Neighborhood I constraint} x1 + x2 + x7 ≥ 1 {Neighborhood J constraint}

53) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model: Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint} x1 + x2 + x3 ≥ 1 {Neighborhood B constraint} x5 + x6 + x8 ≥ 1 {Neighborhood C constraint} x1 + x4 + x7 ≥ 1 {Neighborhood D constraint} x2 + x3 + x7 ≥ 1 {Neighborhood E constraint} x3 + x4 + x8 ≥ 1 {Neighborhood F constraint} x2 + x5 + x7 ≥ 1 {Neighborhood G constraint} x1 + x4 + x6 ≥ 1 {Neighborhood H constraint} x1 + x6 + x8 ≥ 1 {Neighborhood I constraint} x1 + x2 + x7 ≥ 1 {Neighborhood J constraint}

Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations? A) 210 B) 220 C) 265 D) 310 E) 435

54) The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + x6 ≥ 1 {Residence Hall A constraint} x1 + x2 + x3 ≥ 1 {Residence Hall B constraint} x4 + x5 + x6 ≥ 1 {Science building constraint} x1 + x4 + x5 ≥ 1 {Music building constraint} x2 + x3 + x4 ≥ 1 {Math building constraint} x3 + x4 + x5 ≥ 1 {Business building constraint} x2 + x5 + x6 ≥ 1 {Auditorium constraint} x1 + x4 + x6 ≥ 1 {Arena constraint} x1 + x2 + x3 + x4 + x5 + x6 ≥ 4 {Total locations constraint}

55) The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + x6 ≥ 1 {Residence Hall A constraint} x1 + x2 + x3 ≥ 1 {Residence Hall B constraint} x4 + x5 + x6 ≥ 1 {Science building constraint} x1 + x4 + x5 ≥ 1 {Music building constraint} x2 + x3 + x4 ≥ 1 {Math building constraint} x3 + x4 + x5 ≥ 1 {Business building constraint} x2 + x5 + x6 ≥ 1 {Auditorium constraint} x1 + x4 + x6 ≥ 1 {Arena constraint} x1 + x2 + x3 + x4 + x5 + x6 ≥ 4 {Total locations constraint}

Which of the locations is the most expensive? A) Location 2 B) Location 3 C) Location 4 D) Location 5 E) Location 6

56) The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + x6 ≥ 1 {Residence Hall A constraint} x1 + x2 + x3 ≥ 1 {Residence Hall B constraint} x4 + x5 + x6 ≥ 1 {Science building constraint} x1 + x4 + x5 ≥ 1 {Music building constraint} x2 + x3 + x4 ≥ 1 {Math building constraint} x3 + x4 + x5 ≥ 1 {Business building constraint} x2 + x5 + x6 ≥ 1 {Auditorium constraint} x1 + x4 + x6 ≥ 1 {Arena constraint} x1 + x2 + x3 + x4 + x5 + x6 ≥ 4 {Total locations constraint}

57) The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + x6 ≥ 1 {Residence Hall A constraint} x1 + x2 + x3 ≥ 1 {Residence Hall B constraint} x4 + x5 + x6 ≥ 1 {Science building constraint} x1 + x4 + x5 ≥ 1 {Music building constraint} x2 + x3 + x4 ≥ 1 {Math building constraint} x3 + x4 + x5 ≥ 1 {Business building constraint} x2 + x5 + x6 ≥ 1 {Auditorium constraint} x1 + x4 + x6 ≥ 1 {Arena constraint} x1 + x2 + x3 + x4 + x5 + x6 ≥ 4 {Total locations constraint}

Which of the locations is NOT within 5 minutes of the Arena? A) Location 1 B) Location 2 C) Location 4 D) Location 6 E) Location 7

58) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + x6 ≥ 1{Residence Hall A constraint} x1 + x2 + x3 ≥ 1 {Residence Hall B constraint} x4 + x5 + x6 ≥ 1 {Science building constraint} x1 + x4 + x5 ≥ 1 {Music building constraint} x2 + x3 + x4 ≥ 1 {Math building constraint} x3 + x4 + x5 ≥ 1 {Business building constraint} x2 + x5 + x6 ≥ 1 {Auditorium constraint} x1 + x4 + x6 ≥ 1 {Arena constraint} x1 + x2 + x3 + x4 + x5 + x6 ≥ 4 {Total locations constraint}

59) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + x6 ≥ 1 {Residence Hall A constraint} x1 + x2 + x3 ≥ 1 {Residence Hall B constraint} x4 + x5 + x6 ≥ 1 {Science building constraint} x1 + x4 + x5 ≥ 1 {Music building constraint} x2 + x3 + x4 ≥ 1 {Math building constraint} x3 + x4 + x5 ≥ 1 {Business building constraint} x2 + x5 + x6 ≥ 1 {Auditorium constraint} x1 + x4 + x6 ≥ 1 {Arena constraint} x1 + x2 + x3 + x4 + x5 + x6 ≥ 4 {Total locations constraint}

Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations? A) 1,445 B) 1,535 C) 1,655 D) 1,715 E) 1,865

60) The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Building A constraint} x1 + x2 + x3 ≥ 1 {Building B constraint} x6 + x8 ≥ 1 {Building C constraint} x1 + x4 + x7 ≥ 1 {Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 ≥ 1 {Building F constraint} x2 + x5 + x7 ≥ 1 {Building G constraint} x1 + x4 + x6 ≥ 1 {Building H constraint} x1 + x6 + x8 ≥ 1 {Building I constraint} x1 + x2 + x7 ≥ 1 {Building J constraint}

Which of the constraints is a set covering constraint? A) Building A constraint B) Building C constraint C) Building F constraint D) All of the choices are correct. E) None of the choices is correct.

61) The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 200x1 + 250x2 + 225x3 + 190x4 +215x 5 + 245x6 + 235x7 + 220x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Building A constraint} x1 + x2 + x3 ≥ 1 {Building B constraint} x6 + x8 ≥ 1 {Building C constraint} x1 + x4 + x7 ≥ 1 {Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 ≥ 1 {Building F constraint} x2 + x5 + x7 ≥ 1 {Building G constraint} x1 + x4 + x6 ≥ 1 {Building H constraint} x1 + x6 + x8 ≥ 1 {Building I constraint} x1 + x2 + x7 ≥ 1 {Building J constraint}

Which of the crews is the least expensive? A) Crew 1 B) Crew 2 C) Crew 3 D) Crew 4 E) Crew 5

62) The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Building A constraint} x1 + x2 + x3 ≥ 1 {Building B constraint} x6 + x8 ≥ 1 {Building C constraint} x1 + x4 + x7 ≥ 1 {Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 ≥ 1 {Building F constraint} x2 + x5 + x7 ≥ 1 {Building G constraint} x1 + x4 + x6 ≥ 1 {Building H constraint} x1 + x6 + x8 ≥ 1 {Building I constraint} x1 + x2 + x7 ≥ 1 {Building J constraint}

Which of the crews can be scheduled to clean buildings B and F? A) Crew 3 B) Crew 4 C) Crew 6 D) Crew 7 E) Crew 8

63) The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Building A constraint} x1 + x2 + x3 ≥ 1 {Building B constraint} x6 + x8 ≥ 1 {Building C constraint} x1 + x4 + x7 ≥ 1 {Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 ≥ 1 {Building F constraint} x2 + x5 + x7 ≥ 1 {Building G constraint} x1 + x4 + x6 ≥ 1 {Building H constraint} x1 + x6 + x8 ≥ 1 {Building I constraint} x1 + x2 + x7 ≥ 1 {Building J constraint}

Which of the crews can be scheduled to clean building A? A) Crew 1 B) Crew 2 C) Crew 5 D) Crew 6 E) Crew 7

64) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Building A constraint} x1 + x2 + x3 ≥ 1 {Building B constraint} x6 + x8 ≥ 1 {Building C constraint} x1 + x4 + x7 ≥ 1 {Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 ≥ 1 {Building F constraint} x2 + x5 + x7 ≥ 1 {Building G constraint} x1 + x4 + x6 ≥ 1 {Building H constraint} x1 + x6 + x8 ≥ 1 {Building I constraint} x1 + x2 + x7 ≥ 1 {Building J constraint}

Set up the problem in Excel and find the optimal solution. Which crews are selected? A) Crews 1, 2, and 3 B) Crews 1, 5, and 6 C) Crews 1, 7, and 8 D) Crews 2, 3, and 5 E) Crews 3, 4, and 5.

65) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8 s.t. x1 + x2 + x5 + x7 ≥ 1 {Building A constraint} x1 + x2 + x3 ≥ 1 {Building B constraint} x6 + x8 ≥ 1 {Building C constraint} x1 + x4 + x7 ≥ 1 {Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 ≥ 1 {Building F constraint} x2 + x5 + x7 ≥ 1 {Building G constraint} x1 + x4 + x6 ≥ 1 {Building H constraint} x1 + x6 + x8 ≥ 1{Building I constraint} x1 + x2 + x7 ≥ 1 {Building J constraint}

Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations? A) 255 B) 355 C) 455 D) 555 E) 655

66) A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables). The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model: Max 20x1 + 65x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 100 {Constraint 1} 20x1 + 50x2 ≥ 250 {Constraint 2} 1x1 + 1.5x2 ≤ 10 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

Which of the constraints limit the amount of raw materials that can be consumed? A) Constraint 1 B) Constraint 4 C) Constraint 5 D) Constraint 1 and 4 only E) None of these 67) A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables). The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model: Max 20x1 + 65x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 100 {Constraint 1} 20x1 + 50x2 ≥ 250 {Constraint 2} 1x1 + 1.5x2 ≤ 10 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

Which of the following would be a reasonable value for the variable "M"? A) 100 B) 10 C) 1 D) 0.1 E) 0.01

68) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables). The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model: Max 20x1 + 65x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 100 {Constraint 1} 20x1 + 50x2 ≥ 250 {Constraint 2} 1x1 + 1.5x2 ≤ 10 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

69) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables). The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model: Max 20x1 + 65x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 100 {Constraint 1} 20x1 + 50x2 ≥ 250 {Constraint 2} 1x1 + 1.5x2 ≤ 10 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

Set up the problem in Excel and find the optimal solution. What is the maximum profit possible? A) $25 B) $50 C) $75 D) $100 E) $125 70) A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies). The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example): Max 10x1 + 12x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 1000 {Constraint 1} 2x1 + 5x2 ≥ 2500 {Constraint 2} 2x1 + 1x2 ≤ 300 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

71) A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies). The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example): Max 10x1 + 12x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 1000 {Constraint 1} 2x1 + 5x2 ≥ 2500 {Constraint 2} 2x1 + 1x2 ≤ 300 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

Which of the following would be a reasonable value for the variable "M"? A) 0.1 B) 1 C) 10 D) 100 E) 1,000

72) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies). The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example): Max 10x1 + 12x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 1000 {Constraint 1} 2x1 + 5x2 ≥ 2500 {Constraint 2} 2x1 + 1x2 ≤ 300 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

73) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies). The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example): Max 10x1 + 12x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 1000 {Constraint 1} 2x1 + 5x2 ≥ 2500 {Constraint 2} 2x1 + 1x2 ≤ 300 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

Set up the problem in Excel and find the optimal solution. What is the maximum profit possible? A) $1,233.33 B) $1,333.33 C) $1,433.33 D) $1,533.33 E) $1,633.33 74) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. Your employer is trying to select from a list of possible capital projects. The projects, along with their cost and benefits, are listed below. The capital budget available is $1 million. In addition to spending constraints, your employer would like to select at least two projects. If project 1 is chosen then project 2 cannot be selected. Formulate the problem as a linear program and determine the optimal solution. Project 1 2 3 4 5

Cost $ 250,000 $ 500,000 $ 290,000 $ 650,000 $ 750,000

Net Present Value Notes $ 500,000 Cannot be selected if 2 is selected $ 750,000 Cannot be selected if 1 is selected $ 333,000 $ 400,000 $ 600,000

A) Project 1 and project 2 B) Project 1 and project 3 C) Project 1 and project 5 D) Project 2 and project 3 E) Project 3 and project 5

75) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. To enhance the safety of your facility, you decide to add more fire extinguishers. Your goal is to have each area within 50 feet of a fire extinguisher, but to minimize the total number of fire extinguishers you need to purchase. You have divided the facility into 7 zones and have identified 8 possible locations for fire extinguishers. The following table shows the distance (in feet) from each zone to each potential location.

Location 1 Location 2 Location 3 Location 4 Location 5 Location 6 Location 7 Location 8

Distance to location (in feet) Zone A Zone B Zone C Zone D Zone E Zone F Zone G 51 40 70 73 36 32 50 75 40 65 48 52 79 55 58 73 74 64 41 59 67 80 51 52 30 50 64 43 42 38 59 54 41 74 55 53 59 51 46 61 36 47 71 52 62 67 63 62 30 74 68 31 77 60 32 38

How many fire extinguishers should you purchase? A) 2 B) 3 C) 4 D) 5 E) 6 76) A manufacturer produces both widgets and gadgets. Widgets generate a profit of $50 each and gadgets have a profit margin of $35 each. To produce each item, a setup cost is incurred. This setup cost of $500 for widgets and $400 for gadgets. Widgets consume 4 units of raw material A and 5 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 500 units of each raw material available. Set up the problem in Excel and find the optimal solution. What is the maximum profit possible? A) $3,500 B) $4,500 C) $5,500 D) $6,500 E) $7,500

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 7 Using Binary Integer Programming to Deal with Yes-or-No Decisions 1) Binary integer programming problems are those where all the decision variables restricted to integer values are further restricted to be binary variables. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) Binary variables are variables whose only possible values are 0 or 1. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) Variables whose only possible values are 0 and 1 are called integer variables. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) A problems where all the variables are binary variables is called a pure BIP problem. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 1 Copyright © 2019 McGraw-Hill

5) Binary variables are best suited to be the decision variables when dealing with yes-or-no decisions. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) A BIP problem considers one yes-or-no decision at a time with the objective of choosing the best alternative. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) The algorithms available for solving BIP problems are much more efficient than those for linear programming which is one of the advantages of formulating problems this way. Answer: FALSE Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) If choosing one alternative from a group excludes choosing all of the others then these alternatives are called mutually exclusive. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2 Copyright © 2019 McGraw-Hill

9) The constraint x1 + x2 + x3 ≤ 3 in a BIP represents mutually exclusive alternatives. Answer: FALSE Explanation: A mutually exclusive constraint allows at most one alternative to be selected (that is, at most one variable can have a value of 1). The constraint x1 + x2 + x3 ≤ 3 allows selection of 0, 1, 2, or all 3 alternatives simultaneously. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) It is possible to have a constraint in a BIP that excludes the possibility of choosing none of the alternatives available. Answer: TRUE Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) A yes-or-no decision is a mutually exclusive decision if it can be yes only if a certain other yes-or-no decision is yes. Answer: FALSE Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

12) The constraint x1 ≤ x2 in a BIP problem means that alternative 2 cannot be selected unless alternative 1 is also selected. Answer: FALSE Explanation: The constraint x1 ≤ x2 is a contingent constraint. It allows for selection of neither alternative (x1 = x2 = 0), only the second alternative (x1 = 0, x2 = 1), or both alternatives (x1 = x2 = 1). The only action that is not allowed is selection of only the first alternative (x1 = 1, x2 = 0). Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation 13) BIP can be used in capital budgeting decisions to determine whether to invest a certain amount. Answer: TRUE Difficulty: 1 Easy Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) BIP can be used to determine the timing of activities. Answer: TRUE Difficulty: 1 Easy Topic: Using BIP for Crew Scheduling: The Southwestern Airways Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

15) An auxiliary binary variable is an additional binary variable that is introduced into a model to represent additional yes-or-no decisions. Answer: FALSE Difficulty: 1 Easy Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) A linear programming formulation is not valid for a product mix problem when there are setup costs for initiating production. Answer: TRUE Difficulty: 1 Easy Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 17) The Excel sensitivity report can be used to perform sensitivity analysis for integer programming problems. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

18) A parameter analysis report can be used to perform sensitivity analysis for integer programming problems. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) To model a situation where a setup cost will be charged if a certain product is produced, the best approach is to include and Excel "IF" function. Answer: FALSE Difficulty: 1 Easy Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) In a site selection problem, a common goal is to identify the set of locations that provides adequate service at the minimum cost. Answer: TRUE Difficulty: 1 Easy Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

21) In a crew scheduling problem there is no need for a set covering constraint. Answer: FALSE Difficulty: 1 Easy Topic: Using BIP for Crew Scheduling: The Southwestern Airways Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) If activities A and B are mutually exclusive, the constraint xA ≤ xB will enforce this relationship in a linear program. Answer: FALSE Explanation: The constraint xA ≤ xB will enforce a contingent relationship between activities A and B. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) If a firm wishes to choose at most 2 of 4 possible activities (A, B, C and D), the constraint xA + xB + xC + xD ≥ 2 will enforce this relationship in a linear program. Answer: FALSE Explanation: The constraint xA + xB + xC + xD ≥ 2 will ensure that at least 2 of the 4 activities are selected. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

24) If a firm wishes to choose at least 2 of 4 possible activities (A, B, C and D), the constraint xA + xB + xC + xD ≥ 2 will enforce this relationship in a linear program. Answer: FALSE Explanation: The constraint xA + xB + xC + xD ≥ 2 will ensure that at least 2 of the 4 activities are selected. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 25) When binary variables are used in a linear program, the Solver Sensitivity Report is not available. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) Binary integer programming problems can answer which types of questions? A) Should a project be undertaken? B) Should an investment be made? C) Should a plant be located at a particular location? D) All of the choices are correct. E) None of the choices is correct. Answer: D Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

27) Binary variables can have the following values: A) 0 only. B) 1 only. C) any integer value less than 1. D) 0 and 1 only. E) any integer value greater than 1. Answer: D Difficulty: 1 Easy Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) Binary integer programming can be used for: A) capital budgeting. B) site selection. C) scheduling asset divestitures. D) assignments of routes. E) All of the choices are correct. Answer: E Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

29) In a BIP problem with 2 mutually exclusive alternatives, x1 and x2, the following constraint needs to be added to the formulation: A) x1 + x2 ≤ 1. B) x1 + x2 ≥ 1. C) x1 – x2 ≤ 1. D) x1 – x2 = 1. E) None of the choices is correct. Answer: A Explanation: The constraint x1 + x2 ≤ 1 allows at most one of the two options to be selected. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) In a BIP problem with 2 mutually exclusive alternatives, x1 and x2, the following constraint needs to be added to the formulation if one alternative must be chosen: A) x1 + x2 ≤ 1. B) x1 + x2 = 1. C) x1 – x2 ≤ 1. D) x1– x2 = 1. E) None of the choices is correct. Answer: B Explanation: The constraint x1 + x2 = 1 requires that one (and only one) of the two options be selected. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

31) In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If project A can be undertaken only if project B is also undertaken then the following constraint needs to be added to the formulation: A) A + B ≤ 1. B) A + B = 1. C) A ≤ B. D) B ≤ A. E) None of the choices is correct. Answer: C Explanation: The contingent constraint A ≤ B allows project B to be selected independent of A, but requires that B is selected if A will also be selected. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 32) In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If there are two projects under consideration, A and B, and either both projects will be undertaken or no project will be undertaken, then the following constraint needs to be added to the formulation: A) A ≤ B. B) A + B ≤ 2. C) A ≥ B. D) A = B. E) None of the choices is correct. Answer: D Explanation: The contingent constraint A = B requires that either both project be selected (A = B = 1) or that neither project be selected (A = B = 0). Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

33) In a BIP problem with 3 mutually exclusive alternatives, x1, x2, and x3, the following constraint needs to be added to the formulation: A) x1 + x2 + x3 ≤ 1. B) x1 + x2 + x3 = 1. C) x1 – x2 – x3 ≤ 1. D) x1 – x2 – x3 = 1. E) None of the choices is correct. Answer: A Explanation: The mutually exclusive constraint x1 + x2 +x3 ≤ 1 requires that at most one of the projects be selected by allowing at most one of the variables to have a value of 1. Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 34) In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If there are 4 projects under consideration (A, B, C, and D) and at most 2 can be chosen then the following constraint needs to be added to the formulation: A) A + B + C + D ≤ 1. B) A + B + C + D ≤ 2. C) A + B + C + D ≤ 4. D) A + B + C + D = 2. E) None of the choices is correct. Answer: B Explanation: The constraint A + B + C + D ≤ 2 requires that at most two of the projects be selected by allowing at most two of the variables to have a value of 1. Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

35) Which of the following techniques or tools can be used to perform sensitivity analysis for an integer programming problem? I. The sensitivity report. II. Trial-and-error. III. A parameter analysis report. A) I only B) II only C) III only D) I and II only E) All of the choices are correct. Answer: D Difficulty: 2 Medium Topic: A Case Study: The California Manufacturing Co. Problem Learning Objective: Describe how binary decision variables are used to represent yes-or-no decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

36) A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Which of the constraints enforces a mutually exclusive relationship? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: C Explanation: Constraint 3 allows at most one of the two variables to have a value of 1, which is a mutually exclusive relationship. Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the constraints enforces a contingent relationship? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: E Explanation: Constraint 5 requires that option 2 and option 4 will have the same decision. Each option is contingent on the other. Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

38) A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Which of the constraints ensures that at least two of the potential sites will be selected? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: B Explanation: Constraint 2 requires that at least two of the variables have a value of 1. Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which constraint ensures that the firm will not spend more capital than it has available (assume that each potential location has a different cost)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: A Explanation: Since all locations have a different cost, constraint 1 shows each selected location (xj = 1) will consume a limited resource (capital). Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

40) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 20x1 + 30x2 + 10x3 + 15x4 s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5}

Set up the problem in Excel and find the optimal solution. Which locations are selected? A) Location 1 B) Location 2 C) Location 4 D) Locations 2 and 4 E) Locations 1 and 3 Answer: E Explanation: The optimal solution selects locations 1 and 3 for the new warehouses. Difficulty: 3 Hard Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the expected net present value of the optimal solution? A) 20 B) 30 C) 35 D) 40 E) 45 Answer: B Explanation: The optimal solution selects locations 1 and 3 for the new warehouses and has an expected value of 30. Difficulty: 3 Hard Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

42) A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Which of the constraints enforces a contingent relationship? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: E Explanation: Constraint 5 requires that option 1 and option 4 will have the same decision. Each option is contingent on the other. Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

44) A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Which of the constraints ensures that at least two of the potential projects will be selected? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: B Explanation: Constraint 2 requires that at least two of the variables have a value of 1. Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which constraint ensures that the firm will not spend more capital than it has available (assume that each potential project has a different cost)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: A Explanation: Since all projects have a different cost, constraint 1 shows each selected project (xj = 1) will consume a limited resource (capital). Difficulty: 2 Medium Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

46) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5}

Set up the problem in Excel and find the optimal solution. Which projects are selected? A) Project 1 B) Project 2 C) Project 4 D) Projects 2 and 3 E) Projects 1 and 3 Answer: D Explanation: The optimal solution selects projects 2 and 3. Difficulty: 3 Hard Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the expected net present value of the optimal solution? A) 210 B) 220 C) 235 D) 310 E) 435 Answer: A Explanation: The optimal solution selects projects 2 and 3 and has an expected value of 210. Difficulty: 3 Hard Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Which of the constraints is a set covering constraint? A) Neighborhood A constraint B) Neighborhood C constraint C) Neighborhood F constraint D) All of the choices are correct. E) None of the choices is correct. Answer: D Explanation: All of the constraints (with the exception of the binary constraint) are set covering constraints. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the locations is the most expensive? A) Location 1. B) Location 2. C) Location 3. D) Location 4. E) Location 5. Answer: D Explanation: Because the objective is to minimize the cost of locations, the objective function coefficient must represent the cost of each location. Therefore, location 4 (coefficient = 135) is the most expensive of the choices. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the locations is within 15 minutes of neighborhoods C, H, and I? A) Location 2 B) Location 4 C) Location 6 D) Location 8 E) None of these locations is within 15 minutes of neighborhoods C, H, and I. Answer: C Explanation: The variable for location 6 (x6) appears in the set covering constraints for neighborhoods C, H, and I. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the locations is NOT within 15 minutes of neighborhood A? A) Location 1 B) Location 2 C) Location 5 D) Location 6 E) Location 7 Answer: D Explanation: The variable for location 6 (x6) does not appear in the set covering constraint for neighborhood A. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. Which locations are selected? A) Location 1 B) Location 3 C) Location 5 D) None of locations 1, 3, and 5 are selected. E) All of locations 1, 3, and 5 are selected. Answer: E Explanation: The optimal solution selects locations 1, 3, and 5. Difficulty: 3 Hard Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations? A) 210 B) 220 C) 265 D) 310 E) 435 Answer: C Explanation: The optimal solution selects locations 1, 3, and 5 at a cost of 265. Difficulty: 3 Hard Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Which of the constraints is a set covering constraint? I. Residence Hall A constraint. II. Science building constraint. III. Total locations constraint. A) I only B) II only C) III only D) All of these E) I and II only Answer: E Explanation: All of the constraints (with the exception of the binary constraint and the Total locations constraint) are set covering constraints. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the locations is the most expensive? A) Location 2 B) Location 3 C) Location 4 D) Location 5 E) Location 6 Answer: E Explanation: Because the objective is to minimize the cost of locations, the objective function coefficient must represent the cost of each location. Therefore, location 6 (coefficient = 500) is the most expensive of the choices. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the locations is within 5 minutes of the science, music, math, and business buildings? A) Location 2 B) Location 4 C) Location 5 D) Location 6 E) None of these locations is within 5 minutes of the listed buildings. Answer: B Explanation: The variable for location 4 (x4) appears in the set covering constraints for the science, music, math, and business buildings. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the locations is NOT within 5 minutes of the Arena? A) Location 1 B) Location 2 C) Location 4 D) Location 6 E) Location 7 Answer: B Explanation: The variable for location 4 (x4) does not appear in the set covering constraint for the Arena. Difficulty: 2 Medium Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. Which locations are selected? A) Locations 1, 3, 4, and 5 B) Locations 1, 2, 4, and 5 C) Locations 1, 2, 3, and 5 D) Locations 2, 3, 4, and 5 E) Locations 1, 3, and 5 Answer: B Explanation: The optimal solution selects locations 1, 2, 4, and 5. Difficulty: 3 Hard Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations? A) 1,445 B) 1,535 C) 1,655 D) 1,715 E) 1,865 Answer: B Explanation: The optimal solution selects locations 1, 2, 4, and 5 at a cost of 1,535. Difficulty: 3 Hard Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Which of the constraints is a set covering constraint? A) Building A constraint B) Building C constraint C) Building F constraint D) All of the choices are correct. E) None of the choices is correct. Answer: D Explanation: All of the constraints (with the exception of the binary constraint) are set covering constraints. Difficulty: 2 Medium Topic: Using BIP for Crew Scheduling: The Southwestern Airways Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the crews is the least expensive? A) Crew 1 B) Crew 2 C) Crew 3 D) Crew 4 E) Crew 5 Answer: D Explanation: Because the objective is to minimize the cost of crews, the objective function coefficient must represent the cost of each location. Therefore, crew 4 (coefficient = 190) is the least expensive of the choices. Difficulty: 2 Medium Topic: Using BIP for Crew Scheduling: The Southwestern Airways Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the crews can be scheduled to clean buildings B and F? A) Crew 3 B) Crew 4 C) Crew 6 D) Crew 7 E) Crew 8 Answer: A Explanation: The variable for crew 3 (x3) appears in the set covering constraints for buildings B and F. Difficulty: 2 Medium Topic: Using BIP for Crew Scheduling: The Southwestern Airways Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the crews can be scheduled to clean building A? A) Crew 1 B) Crew 2 C) Crew 5 D) Crew 6 E) Crew 7 Answer: D Explanation: The variable for location 6 (x6) does not appear in the set covering constraint for building A. Difficulty: 2 Medium Topic: Using BIP for Crew Scheduling: The Southwestern Airways Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. Which crews are selected? A) Crews 1, 2, and 3 B) Crews 1, 5, and 6 C) Crews 1, 7, and 8 D) Crews 2, 3, and 5 E) Crews 3, 4, and 5. Answer: E Explanation: The optimal solution selects crews 1, 7, and 8. Difficulty: 3 Hard Topic: Using BIP for Crew Scheduling: The Southwestern Airways Problem Learning Objective: Formulate a binary integer programming model for crew scheduling in the travel industry. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations? A) 255 B) 355 C) 455 D) 555 E) 655 Answer: E Explanation: The optimal solution selects crews 1, 7, and 8 at a cost of 655. Difficulty: 3 Hard Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Which of the constraints limit the amount of raw materials that can be consumed? A) Constraint 1 B) Constraint 4 C) Constraint 5 D) Constraint 1 and 4 only E) None of these Answer: A Explanation: Constraints 1, 2, and 3 limit the amount of raw materials that can be consumed to the available quantities. Difficulty: 2 Medium Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

67) A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables). The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model: Max 20x1 + 65x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 100 {Constraint 1} 20x1 + 50x2 ≥ 250 {Constraint 2} 1x1 + 1.5x2 ≤ 10 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

Which of the following would be a reasonable value for the variable "M"? A) 100 B) 10 C) 1 D) 0.1 E) 0.01 Answer: A Explanation: M is a "sufficiently" large number to ensure that Myj will exceed any reasonable decision variable. In this case, production of chairs and tables could reasonably exceed 10, but not 100. Difficulty: 2 Medium Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the optimal production schedule? A) 10 chairs, 0 tables B) 0 chairs, 5 tables C) 10 chairs, 5 tables D) 5 chairs, 10 tables E) 15 chairs, 5 tables Answer: B Explanation: After solving the linear program, the optimal production schedule is 0 chairs and 5 tables. Difficulty: 3 Hard Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the maximum profit possible? A) $25 B) $50 C) $75 D) $100 E) $125 Answer: E Explanation: After solving the linear program, the optimal production schedule is 0 chairs and 5 tables and the profit is $125. Difficulty: 3 Hard Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

70) A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies). The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example): Max 10x1 + 12x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 1000 {Constraint 1} 2x1 + 5x2 ≥ 2500 {Constraint 2} 2x1 + 1x2 ≤ 300 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5}

Which of the constraints limit the amount of raw materials that can be consumed? A) Constraint 3 B) Constraint 4 C) Constraint 5 D) Constraint 3 and 4 E) None of these. Answer: A Explanation: Constraints 1, 2, and 3 limit the amount of raw materials that can be consumed to the available quantities. Difficulty: 2 Medium Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Which of the following would be a reasonable value for the variable "M"? A) 0.1 B) 1 C) 10 D) 100 E) 1,000 Answer: E Explanation: M is a "sufficiently" large number to ensure that Myj will exceed any reasonable decision variable. In this case, production of pies and cakes could reasonably exceed 100, but not 1,000. Difficulty: 2 Medium Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the optimal production schedule? A) 133⅓ cakes, 33⅓ pies B) 133⅓ cakes, 0 pies C) 0 cakes, 33⅓ pies D) 33⅓ cakes, 133⅓ pies E) 133⅓ cakes, 133⅓ pies Answer: A Explanation: After solving the linear program, the optimal production schedule is 133⅓ cakes and 33⅓ pies. Difficulty: 3 Hard Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Set up the problem in Excel and find the optimal solution. What is the maximum profit possible? A) $1,233.33 B) $1,333.33 C) $1,433.33 D) $1,533.33 E) $1,633.33 Answer: C Explanation: After solving the linear program, the optimal production schedule is 133⅓ cakes and 33⅓ pies and the profit is $1,433.33. Difficulty: 3 Hard Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

74) Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver. Your employer is trying to select from a list of possible capital projects. The projects, along with their cost and benefits, are listed below. The capital budget available is $1 million. In addition to spending constraints, your employer would like to select at least two projects. If project 1 is chosen then project 2 cannot be selected. Formulate the problem as a linear program and determine the optimal solution. Project 1 2 3 4 5

Cost $ 250,000 $ 500,000 $ 290,000 $ 650,000 $ 750,000

Net Present Value Notes $ 500,000 Cannot be selected if 2 is selected $ 750,000 Cannot be selected if 1 is selected $ 333,000 $ 400,000 $ 600,000

A) Project 1 and project 2 B) Project 1 and project 3 C) Project 1 and project 5 D) Project 2 and project 3 E) Project 3 and project 5 Answer: C Explanation: Solving the linear program below shows that the optimal solution is to select projects 1 and 5. Max 500x1 + 750x2 + 333x3 + 400x4 + 600x5 s.t. 250x1 + 500x2 + 290x3 + 650x4 +750x5 ≤ 1000 {Capital} x1 + x2 ≤ 1 {Projects 1 and 2 are mutually exclusive} x1 + x2 + x3 + x4 + x5 ≥ 10200 {Select at least two projects}

Difficulty: 3 Hard Topic: Using BIP for Project Selection: The Tazer Corp. Problem Learning Objective: Formulate a binary integer programming model for the selection of projects. Bloom's: Create AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Location 1 Location 2 Location 3 Location 4 Location 5 Location 6 Location 7 Location 8

How many fire extinguishers should you purchase? A) 2 B) 3 C) 4 D) 5 E) 6

Answer: B Explanation: Solving the linear program below shows that the optimal solution is to select locations 2, 5, and 8 (although other optimal solutions may exist, 3 fire extinguishers is the minimum required).

Difficulty: 3 Hard Topic: Using BIP for the Selection of Sites for Emergency Services Facilities: The Caliente City Problem Learning Objective: Formulate a binary integer programming model for the selection of sites for facilities. Bloom's: Create AACSB: Analytical Thinking Accessibility: Keyboard Navigation

76) A manufacturer produces both widgets and gadgets. Widgets generate a profit of $50 each and gadgets have a profit margin of $35 each. To produce each item, a setup cost is incurred. This setup cost of $500 for widgets and $400 for gadgets. Widgets consume 4 units of raw material A and 5 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 500 units of each raw material available. Set up the problem in Excel and find the optimal solution. What is the maximum profit possible? A) $3,500 B) $4,500 C) $5,500 D) $6,500 E) $7,500 Answer: B Explanation: After solving the linear program below, the optimal production schedule is 100 widgets and 0 gadgets, the profit is $4,500. Max 50x1 + 35x2 – 500y1 – 400y2 s.t. 4x1 + 6x2 ≤ 500 {Raw material A} 5x1 + 2x2 ≤ 500 {Raw material B} My1 ≥ x1 {Widget Setup Cost} My2 ≥ x2 {Gadget Setup Cost} Difficulty: 3 Hard Topic: Using Mixed BIP to Deal with Setup Costs for Initiating Production: The Revised Wyndor Problem Learning Objective: Use mixed binary integer programming to deal with setup costs for initiating the production of a product. Bloom's: Analyze AACSB: Technology Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 8 Nonlinear Programming 1) Linear programming assumes that the profit from each activity is proportional to the level of that activity. 2) If the slope of a graph never increases but sometimes decreases as the level of the activity increases, then it is said to have decreasing marginal returns. 3) In problems where the objective is to minimize the total cost of the activities, an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases. 4) If C1:C6 are all changing cells, then SUMPRODUCT(C1:C3, C4:C6) is a linear function. 5) If C1 is a changing cell, then ROUND(C1) is a linear function. 6) If D1 is a data cell, and C1 and C2 are changing cells, then IF(D1 >= 2, C1, C2) is a linear function. 7) Nonlinear programming problems with decreasing marginal returns are generally easier to solve then nonlinear programming problems with increasing marginal returns. 8) Sometimes the Solver can return different solutions when optimizing a nonlinear programming problem. 9) Excel's curve fitting method is used to graph a nonlinear equation. 10) Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data. 11) A local maximum is always a global maximum in a nonlinear programming problem. 12) A quadratic programming problem is a special type of linear programming problem. 13) Having activities with decreasing marginal returns is the only way that the proportionality assumption can be violated. 14) Separable programming is applicable when there are increasing or decreasing marginal returns. 15) In separable programming, each activity that violates the proportionality assumption is separated into parts with a new variable for each part. 16) In some cases of separable programming, the profit graphs will be curves rather than a series of line segments.

17) When the marginal return from an activity decreases on a continuous basis, the profit graphs will consist of a series of line segments. 18) Applying separable programming requires having profit graphs that are smooth curves. 19) A nonlinear function may contain a product of two variables. 20) In separable programming, if an activity violates the proportionality assumption it must have increasing marginal returns. 21) Profit = 3x1 + 2x2 + 9x1x2 is an example of a nonlinear function. 22) The additivity assumption of linear programming states that each term in the objective function is the sum of two or more variables. 23) The additivity assumption can be violated by nonlinear programming because of cross-product terms involving the product of two variables. 24) It now is common practice for professional managers of large stock portfolios to use computer models based partially on separable programming. 25) When applying nonlinear programming to portfolio selection, a trade-off is being made between the expected return and the risk associated with the investment. 26) The risk for a portfolio is decreased when the particular stocks tend to move up and down together. 27) The multistart feature in Solver can be used for nonlinear programming problems to systematically try a number of different starting points. 28) Trying different starting points and picking the best solution will always yield the optimal solution to a nonlinear programming problem. 29) Evolutionary Solver uses an algorithm based on genetics, evolution, and survival of the fittest. 30) Mutation is the technique used to create the next generation of solutions in the Evolutionary Solver. 31) The Nonlinear Solver keeps track of a large set of candidate solutions, called the population. 32) The members of the population used to create the next generation are picked randomly by the Evolutionary Solver. 33) Sometimes Evolutionary Solver will make a random change in a member of the population. 34) Evolutionary Solver is often faster than the standard Solver at solving linear programming problems. 2 Copyright © 2019 McGraw-Hill

35) Two runs of the Evolutionary Solver on the same problem will typically yield the same solution. 36) If the RSPE Model Analysis indicates that the model is a NSP, then the GRG Nonlinear search method is the best one to use. 37) If the RSPE Model Analysis indicates that the model is NLP Convex, then only the Evolutionary Solver can be counted on to yield near optimal solutions. 38) If the data cells are in column D and the changing cells are in column C, which of the following are linear formulas in a spreadsheet? I. =SUMPRODUCT(D1:D6, C1:C6) II. =SUMPRODUCT(C1:C3, C4:C6) III. =SUM(C1:C6) A) I only B) II only C) III only D) I, II, and III E) I and III only 39) If the data cells are in column D and the changing cells are in column C, which of the following are not linear formulas in a spreadsheet? I. =IF(D1 >= 6, C1, C2) II. =ROUND(C3) III. =ABS(C3) A) I only B) II only C) III only D) I, II, and III E) II and III only 40) When there are decreasing marginal returns: A) the slope of the graph never increases but sometimes decreases. B) the slope of the graph never decreases but sometimes increases. C) the graph always consists of a smooth curve. D) the graph always consists of a series of line segments. E) separable programming should not be used. 41) Decreasing marginal returns violates which assumption of linear programming? A) The proportionality assumption B) The divisibility assumption C) The additivity assumption D) All of the choices are correct. E) None of the choices is correct. 3 Copyright © 2019 McGraw-Hill

42) A linear function may contain which of the following? I. A term that contains a single variable with an exponent of 1. II. A term that contains a single variable with an exponent of 2. III. A term that is a constant times the product of two variables. A) I only B) II only C) III only D) I, II, and III E) II and III only 43) A nonlinear function may contain which of the following? I. A term that contains a single variable with an exponent of 1. II. A term that contains a single variable with an exponent of 2. III. A term that is a constant times the product of two variables. A) I only B) II only C) III only D) I, II, and III E) II and III only 44) Which of the following can be part of a nonlinear profit graph? I. Decreasing marginal returns. II. Increasing marginal returns. III. Discontinuities. A) I only B) II only C) III only D) I, II, and III E) I and II only 45) A nonlinear programming problem may have: I. Activities with increasing marginal returns. II. Activities with decreasing marginal returns. III. Nonlinear functional constraints. A) I only B) II only C) III only D) I, II, and III E) II and III only

46) Which of the following is an example of a nonlinear function? A) Profit = 5x-1 + 7x2 − 2x22 B) Profit = 8x1x2 − x12 − 4x22 C) Profit = x1 + 6x2 + 3x1x2 D) All of the choices are correct. E) None of the choices is correct. 47) The requirement that each term in the objective function only contains a single variable is in a linear program is referred to as: A) the proportionality assumption. B) the divisibility assumption. C) the additivity assumption. D) a nonlinear function. E) None of the choices is correct. 48) The measure of risk in a portfolio selection problem is called: A) the covariance of the return. B) the variance of the return. C) the expected return. D) decreasing marginal return. E) None of the choices is correct. 49) The measure of risk for pairs of stocks in a portfolio selection problem is called: A) the covariance of the return. B) the variance of the return. C) the expected return. D) decreasing marginal return. E) None of the choices is correct. 50) Separable programming will always find the optimal solution when the following is true: A) The profit or cost graph is piecewise linear. B) There are decreasing marginal returns. C) The profit or cost graph is piecewise linear and there are decreasing marginal returns must both be true. D) Separable programming only finds an approximate solution. E) None of the choices is correct.

51) Which of the following techniques is appropriate when a nonlinear programming problem has multiple local optima? I. Running Solver many times with different starting points. II. Using the multistart feature to try different starting points. III. Using Evolutionary Solver. A) I only B) II only C) III only D) I, II, and III E) II and III only 52) Evolutionary Solver is based on which of the following concepts? I. Genetics. II. Evolution. III. Survival of the Fittest. A) I only B) II only C) III only D) I, II, and III E) II and III only 53) Evolutionary Solver is best suited to which kinds of problems? A) Linear programs B) Nonlinear programs with difficult objective functions C) Nonlinear programs with decreasing marginal returns and no discontinuities D) Nonlinear programs with many constraints E) None of the choices is correct. 54) Which of the following are advantages of the Evolutionary Solver? A) The complexity of the objective function does not matter. B) It will always find the optimal solution. C) It is faster than the standard Solver. D) It always finds the same solution. E) None of the choices is correct. 55) Which of the following are disadvantages of the Evolutionary Solver? I. It does not deal well with complicated objective functions. II. It does perform well on models with many constraints. III. It is easily trapped at local optima. A) I only B) II only C) III only D) I and II E) None of these 6 Copyright © 2019 McGraw-Hill

59) The following chart shows a relationship between advertising expenditures and sales.

60) The following chart shows a relationship between advertising expenditures and sales.

Which of the following describes the chart in terms of a linear relationship? A) The chart shows a linear relationship. B) The chart shows increasing marginal returns. C) The chart shows a proportional relationship. D) The chart shows discontinuities. E) The chart is piecewise linear. 61) Which of the following profit functions has a quadratic form? I. x2 + 3x − 4 II. 3x2 + 4x + 6 III. 3x − 4 A) I only B) II only C) III only D) I and II only E) I, II, and III

62) Which of the following profit functions has a logarithmic form? I. x2 + 3x − 4 II. 4 ln x + 7 III. 3x − 4 A) I only B) II only C) III only D) I and II only E) I, II, and III 63) After some experimentation, you have observed the following data concerning the relationship between marketing and sales. Use Excel's curve fitting method to find the best quadratic equation to model this relationship. Marketing ($) Sales ($100)

100

110

120

130

140

150

160

170

310

400

500

600

700

850

975

1,100

180

190

200

1,300 1,425 1,600

A) 0.11x2 + 1.4x + 40 B) 0.05x2 − 1.1x − 44 C) 0.05x2 + 1.1x + 44 D) 0.11x2 − 1.4x − 40 E) 0.05x2 − 1.1x + 44 64) After some experimentation, you have observed the following data concerning the relationship between marketing and sales. Use Excel's curve fitting method to find the best quadratic equation to model this relationship. Marketing ($) Sales ($100)

100

110

120

130

140

150

160

170

310

500

600

690

780

850

925

1,000

A) −0.055x2 + 24x − 1516 B) 0.055x2 + 24x − 1516 C) −0.055x2 − 24x − 1516 D) −0.055x2 + 24x + 1516 E) −0.11x2 + 24x − 1516

180

190

200

1,050 1,090 1,120

65) The following chart shows the relationship between marketing and sales.

66) The following chart shows the relationship between marketing and sales.

Which of the following statements is TRUE? I. There is a local maximum when marketing expenditure equals $120. II. There is a local minimum when marketing expenditure equals $140. III. There is a local maximum when marketing expenditure equals $160. A) I only B) II only C) III only D) Only I and II E) I, II, and III 67) Which of the following statements about solving maximization problems with Excel's Nonlinear Solver? I. Nonlinear Solver will always find the global maximum. II. Nonlinear Solver will always find a local maximum but not necessarily the global maximum. III. With diminishing returns, Nonlinear Solver will always find the global maximum. A) I only B) II only C) III only D) Only II and III E) I, II, and III

68) If a problem can be modelled as a separable program with three line segments, how many decision variables is it likely to have? A) 1 B) 2 C) 3 D) Only 1 or 2 E) 1, 2, or 3 69) Which of the following statements about Solver's Multistart option are TRUE? A) A nonlinear problem will always have the solution for any starting point. B) Multistart always uses 100 random starting points. C) Using Multistart guarantees that Solver will find the optimal solution. D) Multistart may not find the optimal solution. E) Multistart works well with functions such as "IF" and "ROUND." 70) Note: This problem requires Excel. The marketing department has determined that the relationship between marketing expenditures (x) and sales can be modelled by the equation Sales = 100x − x2 + 20. Use a Nonlinear Solver tool to determine the level of marketing expenditure that will maximize sales. A) 40 B) 50 C) 60 D) 70 E) 80 71) Note: This problem requires Excel. You have noticed that paying higher wages attracts more productive employees. However, you are concerned that there may be a limit to this relationship. Some experimentation has convinced you that the relationship between wages paid (x) and profits can be modelled by the equation Profit = 25x − 0.1x2 + 200. Use a Nonlinear Solver tool to determine the level of wages that will maximize profits. A) 25 B) 50 C) 75 D) 100 E) 125

72) Note: This problem requires Excel. You have noticed that paying higher wages attracts more productive employees. However, you are concerned that there may be a limit to this relationship. Some experimentation has convinced you that the relationship between daily wages paid (x) and profits can be modelled by the equation Profit = 50x − 0.5x2 + .001x3 + 200. The range of wages you are willing to consider is from $0 to $500 per day. Use the Evolutionary Solver tool to determine the level of wages that will maximize profits. A) 200 B) 300 C) 400 D) 500 E) Cannot be determined 73) Note: This problem requires Excel. A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $10 each for the first 50 units, $9 each for units 51-100, and $8 for each unit over 100. Product 2's profitability is $20 each for the first 25 units, $19 each for units 26-50, and $18 each for each unit over 50. The products each require 3 raw materials to produce (see table below for usages and available quantities). Raw Material A B C

Product 1 usage (pounds per unit)

Product 2 usage (pounds per unit) 5 4 7

Available Quantity (pounds) 12 1,000 10 2,000 6 1,500

74) Note: This problem requires Excel. A firm offers two different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $75 each for the first 25 units and $60 for each unit over 25. Product 2's profitability is $200 each for the first 50 units and $100 each for each unit over 50. The products each require two raw materials to produce (see table below for usages and available quantities). Raw Material A B

Product 1 usage (gallons per unit)

Product 2 usage (gallons per unit) 10 5

Available Quantity (gallons) 20 1,500 7 2,000

Use separable programming to find the optimal production plan. A) 100 units Product 1, 100 units Product 2 B) 50 units Product 1, 50 units Product 2 C) 100 units Product 1, 25 units Product 2 D) 25 units Product 1, 100 units Product 2 E) 100 units Product 1, 50 units Product 2 75) If the RSPE Model Analysis indicates that the model is quadratic, which of the following is TRUE? A) The model can be solved using linear programming tools. B) The Evolutionary Solver will always find the optimal solution. C) Using the Nonlinear Solver will never find the optimal solution. D) The model contains functions such as "IF" or "ROUND." E) None of the choices is true.

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 8 Nonlinear Programming 1) Linear programming assumes that the profit from each activity is proportional to the level of that activity. Answer: TRUE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Describe how a nonlinear programming model differs from a linear programming model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) If the slope of a graph never increases but sometimes decreases as the level of the activity increases, then it is said to have decreasing marginal returns. Answer: TRUE Difficulty: 1 Easy Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) In problems where the objective is to minimize the total cost of the activities, an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases. Answer: FALSE Difficulty: 1 Easy Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

4) If C1:C6 are all changing cells, then SUMPRODUCT(C1:C3, C4:C6) is a linear function. Answer: FALSE Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 5) If C1 is a changing cell, then ROUND(C1) is a linear function. Answer: FALSE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) If D1 is a data cell, and C1 and C2 are changing cells, then IF(D1 >= 2, C1, C2) is a linear function. Answer: TRUE Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) Nonlinear programming problems with decreasing marginal returns are generally easier to solve then nonlinear programming problems with increasing marginal returns. Answer: TRUE Difficulty: 1 Easy Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

8) Sometimes the Solver can return different solutions when optimizing a nonlinear programming problem. Answer: TRUE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 9) Excel's curve fitting method is used to graph a nonlinear equation. Answer: FALSE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data. Answer: TRUE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) A local maximum is always a global maximum in a nonlinear programming problem. Answer: FALSE Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

12) A quadratic programming problem is a special type of linear programming problem. Answer: FALSE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 13) Having activities with decreasing marginal returns is the only way that the proportionality assumption can be violated. Answer: FALSE Difficulty: 1 Easy Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) Separable programming is applicable when there are increasing or decreasing marginal returns. Answer: FALSE Difficulty: 1 Easy Topic: Separable Programming Learning Objective: Use the Nonlinear Solver to solve simple types of nonlinear programming problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) In separable programming, each activity that violates the proportionality assumption is separated into parts with a new variable for each part. Answer: TRUE Difficulty: 2 Medium Topic: Separable Programming Learning Objective: Construct nonlinear formulas needed for nonlinear programming models. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

16) In some cases of separable programming, the profit graphs will be curves rather than a series of line segments. Answer: TRUE Difficulty: 1 Easy Topic: Separable Programming Learning Objective: Construct nonlinear formulas needed for nonlinear programming models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 17) When the marginal return from an activity decreases on a continuous basis, the profit graphs will consist of a series of line segments. Answer: FALSE Difficulty: 1 Easy Topic: Separable Programming Learning Objective: Construct nonlinear formulas needed for nonlinear programming models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) Applying separable programming requires having profit graphs that are smooth curves. Answer: FALSE Difficulty: 2 Medium Topic: Separable Programming Learning Objective: Construct nonlinear formulas needed for nonlinear programming models. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) A nonlinear function may contain a product of two variables. Answer: TRUE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

20) In separable programming, if an activity violates the proportionality assumption it must have increasing marginal returns. Answer: FALSE Difficulty: 2 Medium Topic: Separable Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 21) Profit = 3x1 + 2x2 + 9x1x2 is an example of a nonlinear function. Answer: TRUE Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) The additivity assumption of linear programming states that each term in the objective function is the sum of two or more variables. Answer: FALSE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Describe how a nonlinear programming model differs from a linear programming model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) The additivity assumption can be violated by nonlinear programming because of crossproduct terms involving the product of two variables. Answer: TRUE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6 Copyright © 2019 McGraw-Hill

24) It now is common practice for professional managers of large stock portfolios to use computer models based partially on separable programming. Answer: FALSE Difficulty: 1 Easy Topic: Separable Programming Learning Objective: Distinguish between nonlinear programming problems that should be easy to solve and those that may be difficult (if not impossible) to solve. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 25) When applying nonlinear programming to portfolio selection, a trade-off is being made between the expected return and the risk associated with the investment. Answer: TRUE Difficulty: 1 Easy Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Formulate a nonlinear programming model from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) The risk for a portfolio is decreased when the particular stocks tend to move up and down together. Answer: FALSE Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Formulate a nonlinear programming model from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) The multistart feature in Solver can be used for nonlinear programming problems to systematically try a number of different starting points. Answer: TRUE Difficulty: 1 Easy Topic: Difficult Nonlinear Programming Problems Learning Objective: Use the multistart feature of Solver to attempt to solve some more difficult nonlinear programming problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7 Copyright © 2019 McGraw-Hill

28) Trying different starting points and picking the best solution will always yield the optimal solution to a nonlinear programming problem. Answer: FALSE Difficulty: 2 Medium Topic: Difficult Nonlinear Programming Problems Learning Objective: Use the multistart feature of Solver to attempt to solve some more difficult nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 29) Evolutionary Solver uses an algorithm based on genetics, evolution, and survival of the fittest. Answer: TRUE Difficulty: 1 Easy Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) Mutation is the technique used to create the next generation of solutions in the Evolutionary Solver. Answer: FALSE Difficulty: 1 Easy Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) The Nonlinear Solver keeps track of a large set of candidate solutions, called the population. Answer: FALSE Difficulty: 1 Easy Topic: The Challenges of Nonlinear Programming Learning Objective: Use the Nonlinear Solver to solve simple types of nonlinear programming problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

32) The members of the population used to create the next generation are picked randomly by the Evolutionary Solver. Answer: FALSE Difficulty: 2 Medium Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 33) Sometimes Evolutionary Solver will make a random change in a member of the population. Answer: TRUE Difficulty: 1 Easy Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 34) Evolutionary Solver is often faster than the standard Solver at solving linear programming problems. Answer: FALSE Difficulty: 1 Easy Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) Two runs of the Evolutionary Solver on the same problem will typically yield the same solution. Answer: FALSE Difficulty: 2 Medium Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

36) If the RSPE Model Analysis indicates that the model is a NSP, then the GRG Nonlinear search method is the best one to use. Answer: FALSE Difficulty: 2 Medium Topic: Using Analytic Solver To Analyze A Model And Choose A Solving Method Learning Objective: Use Analytic Solver to analyze a model and choose the most appropriate solving method. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 37) If the RSPE Model Analysis indicates that the model is NLP Convex, then only the Evolutionary Solver can be counted on to yield near optimal solutions. Answer: FALSE Difficulty: 2 Medium Topic: Using Analytic Solver To Analyze A Model And Choose A Solving Method Learning Objective: Use Analytic Solver to analyze a model and choose the most appropriate solving method. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) If the data cells are in column D and the changing cells are in column C, which of the following are linear formulas in a spreadsheet? I. =SUMPRODUCT(D1:D6, C1:C6) II. =SUMPRODUCT(C1:C3, C4:C6) III. =SUM(C1:C6) A) I only B) II only C) III only D) I, II, and III E) I and III only Answer: E Explanation: Choice "II only" involves the product of two or more changing cells, which is nonlinear. Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

39) If the data cells are in column D and the changing cells are in column C, which of the following are not linear formulas in a spreadsheet? I. =IF(D1 >= 6, C1, C2) II. =ROUND(C3) III. =ABS(C3) A) I only B) II only C) III only D) I, II, and III E) II and III only Answer: E Explanation: "IF" functions which test a data cell are linear, but the "ROUND" and "ABS" functions are nonlinear. Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 40) When there are decreasing marginal returns: A) the slope of the graph never increases but sometimes decreases. B) the slope of the graph never decreases but sometimes increases. C) the graph always consists of a smooth curve. D) the graph always consists of a series of line segments. E) separable programming should not be used. Answer: A Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

41) Decreasing marginal returns violates which assumption of linear programming? A) The proportionality assumption B) The divisibility assumption C) The additivity assumption D) All of the choices are correct. E) None of the choices is correct. Answer: A Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 42) A linear function may contain which of the following? I. A term that contains a single variable with an exponent of 1. II. A term that contains a single variable with an exponent of 2. III. A term that is a constant times the product of two variables. A) I only B) II only C) III only D) I, II, and III E) II and III only Answer: A Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

43) A nonlinear function may contain which of the following? I. A term that contains a single variable with an exponent of 1. II. A term that contains a single variable with an exponent of 2. III. A term that is a constant times the product of two variables. A) I only B) II only C) III only D) I, II, and III E) II and III only Answer: D Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 44) Which of the following can be part of a nonlinear profit graph? I. Decreasing marginal returns. II. Increasing marginal returns. III. Discontinuities. A) I only B) II only C) III only D) I, II, and III E) I and II only Answer: D Difficulty: 2 Medium Topic: Separable Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

45) A nonlinear programming problem may have: I. Activities with increasing marginal returns. II. Activities with decreasing marginal returns. III. Nonlinear functional constraints. A) I only B) II only C) III only D) I, II, and III E) II and III only Answer: D Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 46) Which of the following is an example of a nonlinear function? A) Profit = 5x-1 + 7x2 − 2x22 B) Profit = 8x1x2 − x12 − 4x22 C) Profit = x1 + 6x2 + 3x1x2 D) All of the choices are correct. E) None of the choices is correct. Answer: E Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

47) The requirement that each term in the objective function only contains a single variable is in a linear program is referred to as: A) the proportionality assumption. B) the divisibility assumption. C) the additivity assumption. D) a nonlinear function. E) None of the choices is correct. Answer: C Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 48) The measure of risk in a portfolio selection problem is called: A) the covariance of the return. B) the variance of the return. C) the expected return. D) decreasing marginal return. E) None of the choices is correct. Answer: B Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Use the Nonlinear Solver to solve simple types of nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 49) The measure of risk for pairs of stocks in a portfolio selection problem is called: A) the covariance of the return. B) the variance of the return. C) the expected return. D) decreasing marginal return. E) None of the choices is correct. Answer: A Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Use the Nonlinear Solver to solve simple types of nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 15 Copyright © 2019 McGraw-Hill

50) Separable programming will always find the optimal solution when the following is true: A) The profit or cost graph is piecewise linear. B) There are decreasing marginal returns. C) The profit or cost graph is piecewise linear and there are decreasing marginal returns must both be true. D) Separable programming only finds an approximate solution. E) None of the choices is correct. Answer: C Difficulty: 2 Medium Topic: Separable Programming Learning Objective: Construct nonlinear formulas needed for nonlinear programming models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 51) Which of the following techniques is appropriate when a nonlinear programming problem has multiple local optima? I. Running Solver many times with different starting points. II. Using the multistart feature to try different starting points. III. Using Evolutionary Solver. A) I only B) II only C) III only D) I, II, and III E) II and III only Answer: D Difficulty: 2 Medium Topic: Difficult Nonlinear Programming Problems Learning Objective: Use the multistart feature of Solver to attempt to solve some more difficult nonlinear programming problems. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

52) Evolutionary Solver is based on which of the following concepts? I. Genetics. II. Evolution. III. Survival of the Fittest. A) I only B) II only C) III only D) I, II, and III E) II and III only Answer: D Difficulty: 2 Medium Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 53) Evolutionary Solver is best suited to which kinds of problems? A) Linear programs B) Nonlinear programs with difficult objective functions C) Nonlinear programs with decreasing marginal returns and no discontinuities D) Nonlinear programs with many constraints E) None of the choices is correct. Answer: B Difficulty: 2 Medium Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

54) Which of the following are advantages of the Evolutionary Solver? A) The complexity of the objective function does not matter. B) It will always find the optimal solution. C) It is faster than the standard Solver. D) It always finds the same solution. E) None of the choices is correct. Answer: A Difficulty: 2 Medium Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 55) Which of the following are disadvantages of the Evolutionary Solver? I. It does not deal well with complicated objective functions. II. It does perform well on models with many constraints. III. It is easily trapped at local optima. A) I only B) II only C) III only D) I and II E) None of these Answer: B Difficulty: 2 Medium Topic: Evolutionary Solver And Genetic Algorithms Learning Objective: Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

56) If a model uses IF or ROUND functions that incorporate the changing cells, then running the RSPE Analyze Model without Solving feature will typically say the model is of what type? A) Linear B) NLP Convex C) QP Convex D) NSP E) None of the choices is correct. Answer: D Difficulty: 2 Medium Topic: Using Analytic Solver To Analyze A Model And Choose A Solving Method Learning Objective: Use Analytic Solver to analyze a model and choose the most appropriate solving method. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 57) One reason that a manager may choose to use a nonlinear model to analyze a problem is A) Nonlinear models are easier to solve than linear models. B) Nonlinear models may provide greater precision than linear models. C) Nonlinear techniques such as Evolutionary Solver provide optimal results. D) Nonlinear models are easier to understand than linear models. E) Nonlinear models take less time to solve than linear models. Answer: B Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Describe how a nonlinear programming model differs from a linear programming model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

58) The following chart shows a relationship between advertising expenditures and sales.

Which of the following describes the chart in terms of a linear relationship? A) The chart shows a linear relationship. B) The chart shows decreasing marginal returns. C) The chart shows a proportional relationship. D) The chart shows discontinuities. E) The chart is piecewise linear. Answer: D Difficulty: 3 Hard Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

59) The following chart shows a relationship between advertising expenditures and sales.

Which of the following describes the chart in terms of a linear relationship? A) The chart shows a linear relationship. B) The chart shows decreasing marginal returns. C) The chart shows a proportional relationship. D) The chart shows increasing marginal returns. E) The chart is piecewise linear. Answer: B Difficulty: 3 Hard Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

60) The following chart shows a relationship between advertising expenditures and sales.

Which of the following describes the chart in terms of a linear relationship? A) The chart shows a linear relationship. B) The chart shows increasing marginal returns. C) The chart shows a proportional relationship. D) The chart shows discontinuities. E) The chart is piecewise linear. Answer: E Difficulty: 3 Hard Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

61) Which of the following profit functions has a quadratic form? I. x2 + 3x − 4 II. 3x2 + 4x + 6 III. 3x − 4 A) I only B) II only C) III only D) I and II only E) I, II, and III Answer: D Explanation: The quadratic form is ax2 + bx + c. Options I and II follow this form. Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 62) Which of the following profit functions has a logarithmic form? I. x2 + 3x − 4 II. 4 ln x + 7 III. 3x − 4 A) I only B) II only C) III only D) I and II only E) I, II, and III Answer: B Explanation: The quadratic form is a In x + b. Option II follows this form. Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

63) After some experimentation, you have observed the following data concerning the relationship between marketing and sales. Use Excel's curve fitting method to find the best quadratic equation to model this relationship. Marketing ($) Sales ($100)

100

110

120

130

140

150

160

170

310

400

500

600

700

850

975

1,100

180

190

200

1,300 1,425 1,600

A) 0.11x2 + 1.4x + 40 B) 0.05x2 − 1.1x − 44 C) 0.05x2 + 1.1x + 44 D) 0.11x2 − 1.4x − 40 E) 0.05x2 − 1.1x + 44 Answer: B Explanation: The best fit using a quadratic form is 0.0469x2 − 1.1416x − 43.904. Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Construct nonlinear formulas needed for nonlinear programming models. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

64) After some experimentation, you have observed the following data concerning the relationship between marketing and sales. Use Excel's curve fitting method to find the best quadratic equation to model this relationship. Marketing ($) Sales ($100)

100

110

120

130

140

150

160

170

310

500

600

690

780

850

925

1,000

180

190

200

1,050 1,090 1,120

A) −0.055x2 + 24x − 1516 B) 0.055x2 + 24x − 1516 C) −0.055x2 − 24x − 1516 D) −0.055x2 + 24x + 1516 E) −0.11x2 + 24x − 1516 Answer: A Explanation: The best fit using a quadratic form is −0.055x2 + 24x − 1516. Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Construct nonlinear formulas needed for nonlinear programming models. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation

65) The following chart shows the relationship between marketing and sales.

Which of the following statements is TRUE? I. There is a local minimum when marketing expenditure equals $120. II. There is a local maximum when marketing expenditure equals $120. III. There is a global maximum when marketing expenditure equals $160. A) I only B) II only C) III only D) I and II only E) II and III only Answer: E Explanation: There is a local maximum when marketing equals 120 (there is a peak but it is lower than the peak when marketing equals 160). There is a global maximum when marketing equals 160 because this is the highest value observed. Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 26 Copyright © 2019 McGraw-Hill

66) The following chart shows the relationship between marketing and sales.

Which of the following statements is TRUE? I. There is a local maximum when marketing expenditure equals $120. II. There is a local minimum when marketing expenditure equals $140. III. There is a local maximum when marketing expenditure equals $160. A) I only B) II only C) III only D) Only I and II E) I, II, and III Answer: E Explanation: There is a local maximum when marketing equals 120 (there is a peak but it is lower than the peak when marketing equals 160). There is a local maximum when marketing equals 160 because this is the highest value observed (this point is also the global maximum). There is a local minimum when marketing equals 140. Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Recognize when a nonlinear programming model is needed to represent a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

67) Which of the following statements about solving maximization problems with Excel's Nonlinear Solver? I. Nonlinear Solver will always find the global maximum. II. Nonlinear Solver will always find a local maximum but not necessarily the global maximum. III. With diminishing returns, Nonlinear Solver will always find the global maximum. A) I only B) II only C) III only D) Only II and III E) I, II, and III Answer: D Explanation: In a maximization problem, Nonlinear Solver will always find a local maximum, but only when marginal returns are decreasing will this be guaranteed to be the global maximum. Difficulty: 2 Medium Topic: The Challenges of Nonlinear Programming Learning Objective: Use the Nonlinear Solver to solve simple types of nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 68) If a problem can be modelled as a separable program with three line segments, how many decision variables is it likely to have? A) 1 B) 2 C) 3 D) Only 1 or 2 E) 1, 2, or 3 Answer: C Explanation: A separable program will have one decision variable for each line segment. Difficulty: 2 Medium Topic: Separable Programming Learning Objective: Recognize when the separable programming technique is applicable to enable using linear programming with a nonlinear objective function. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

69) Which of the following statements about Solver's Multistart option are TRUE? A) A nonlinear problem will always have the solution for any starting point. B) Multistart always uses 100 random starting points. C) Using Multistart guarantees that Solver will find the optimal solution. D) Multistart may not find the optimal solution. E) Multistart works well with functions such as "IF" and "ROUND." Answer: D Difficulty: 2 Medium Topic: Difficult Nonlinear Programming Problems Learning Objective: Use the multistart feature of Solver to attempt to solve some more difficult nonlinear programming problems. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 70) Note: This problem requires Excel. The marketing department has determined that the relationship between marketing expenditures (x) and sales can be modelled by the equation Sales = 100x − x2 + 20. Use a Nonlinear Solver tool to determine the level of marketing expenditure that will maximize sales. A) 40 B) 50 C) 60 D) 70 E) 80 Answer: B Explanation: Since the relationship displays decreasing marginal returns, Nonlinear Solver can be used to find the solution to the following problem: Max 100x − x2 + 20 s.t.x ≥ 0 The optimal solution is x = 50. Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Formulate a nonlinear programming model from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

71) Note: This problem requires Excel. You have noticed that paying higher wages attracts more productive employees. However, you are concerned that there may be a limit to this relationship. Some experimentation has convinced you that the relationship between wages paid (x) and profits can be modelled by the equation Profit = 25x − 0.1x2 + 200. Use a Nonlinear Solver tool to determine the level of wages that will maximize profits. A) 25 B) 50 C) 75 D) 100 E) 125 Answer: E Explanation: Since the relationship displays decreasing marginal returns, Nonlinear Solver can be used to find the solution to the following problem: Max 25x − 0.1x2 + 200 s.t.x ≥ 0 The optimal solution is x = 125. Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Formulate a nonlinear programming model from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

72) Note: This problem requires Excel. You have noticed that paying higher wages attracts more productive employees. However, you are concerned that there may be a limit to this relationship. Some experimentation has convinced you that the relationship between daily wages paid (x) and profits can be modelled by the equation Profit = 50x − 0.5x2 + .001x3 + 200. The range of wages you are willing to consider is from $0 to $500 per day. Use the Evolutionary Solver tool to determine the level of wages that will maximize profits. A) 200 B) 300 C) 400 D) 500 E) Cannot be determined Answer: D Explanation: Since the relationship displays decreasing marginal returns, Nonlinear Solver can be used to find the solution to the following problem: Max 50x − 0.5x2 + 0.001x3 + 200 s.t.x ≥ 0, x ≤ 500 The optimal solution is x = 500. Difficulty: 2 Medium Topic: Nonlinear Programming With Decreasing Marginal Returns Learning Objective: Formulate a nonlinear programming model from a description of the problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

73) Note: This problem requires Excel. A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $10 each for the first 50 units, $9 each for units 51-100, and $8 for each unit over 100. Product 2's profitability is $20 each for the first 25 units, $19 each for units 26-50, and $18 each for each unit over 50. The products each require 3 raw materials to produce (see table below for usages and available quantities). Raw Material A B C

Product 1 usage (pounds per unit)

Product 2 usage (pounds per unit) 5 4 7

Available Quantity (pounds) 12 1,000 10 2,000 6 1,500

Use separable programming to find the optimal production plan. A) 100 units Product 1, 100 units Product 2 B) 100 units Product 1, 50 units Product 2 C) 140 units Product 1, 25 units Product 2 D) 25 units Product 1, 140 units Product 2 E) 100 units Product 1, 140 units Product 2 Answer: C Explanation: The solution to the separable program (see below) shows that the optimal production plan is 140 units of product 1 and 25 units of product 2. Max 10x11 + 9x12 + 8x13 + 20x21 + 19x22 +18x23 s.t. 5x11 + 5x12 + 5x13 + 12x21 +12x22 +12x23 ≤ 1,000 4x11 + 4x12 + 4x13 + 10x21 + 10x22 + 10x23 ≤ 2,000 7x11 + 7x12 + 7x13 + 6x21 + 6x22 + 6x23 ≤ 1,500 0 ≤ x11 ≤ 50 0 ≤ x12 ≤ 50 0 ≤ x13 ≤ ∞ 0 ≤ x21 ≤ 25 0 ≤ x22 ≤ 25 0 ≤ x23 ≤ ∞ Difficulty: 3 Hard Topic: Separable Programming Learning Objective: Apply the separable programming technique when applicable. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation

Product 1 usage (gallons per unit)

Product 2 usage (gallons per unit) 10 5

Available Quantity (gallons) 20 1,500 7 2,000

Use separable programming to find the optimal production plan. A) 100 units Product 1, 100 units Product 2 B) 50 units Product 1, 50 units Product 2 C) 100 units Product 1, 25 units Product 2 D) 25 units Product 1, 100 units Product 2 E) 100 units Product 1, 50 units Product 2 Answer: B Explanation: The solution to the separable program (see below) shows that the optimal production plan is 50 units of product 1 and 50 units of product 2. Max 75x11 + 60x12 + 200x21 + 100x22 s.t. 10x11 + 10x12 + 20x21 + 20x22 ≤ 1,500 5x11 + 5x12 + 7x21 + 7x22 ≤ 2,000 0 ≤ x11 ≤ 25 0 ≤ x12 ≤ ∞ 0 ≤ x21 ≤ 50 0 ≤ x22 ≤ ∞ Difficulty: 3 Hard Topic: Separable Programming Learning Objective: Apply the separable programming technique when applicable. Bloom's: Evaluate AACSB: Technology Accessibility: Keyboard Navigation

75) If the RSPE Model Analysis indicates that the model is quadratic, which of the following is TRUE? A) The model can be solved using linear programming tools. B) The Evolutionary Solver will always find the optimal solution. C) Using the Nonlinear Solver will never find the optimal solution. D) The model contains functions such as "IF" or "ROUND." E) None of the choices is true. Answer: E Explanation: A quadratic model cannot be solved using linear programming tools and the Evolutionary Solver is not guaranteed to find the optimal solution. A quadratic model cannot contain functions such as "IF" or "ROUND," but if the model is being maximized and has diminishing returns, the Nonlinear Solver can find the optimal solution. Difficulty: 2 Medium Topic: Using Analytic Solver To Analyze A Model And Choose A Solving Method Learning Objective: Use Analytic Solver to analyze a model and choose the most appropriate solving method. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 9 Decision Analysis 1) States of nature are alternatives available to a decision maker. 2) In decision analysis, states of nature refer to possible future conditions. 3) Prior probabilities refer to the relative likelihood of possible states of nature. 4) Payoffs always represent profits in decision analysis problems. 5) A decision tree branches out all of the possible decisions and all of the possible events. 6) An advantage of payoff tables compared to decision trees is that they permit us to analyze situations involving sequential decisions. 7) Payoff tables may include only non-negative numbers. 8) A event node in a decision tree indicates that a decision needs to be made at that point. 9) The maximax approach is an optimistic strategy. 10) An example of maximax decision making is a person buying lottery tickets in hopes of a very big payoff. 11) The maximin approach involves choosing the alternative with the highest payoff. 12) The maximin criterion is an optimistic criterion. 13) The maximin approach involves choosing the alternative that has the "best worst" payoff. 14) The maximum likelihood criterion says to focus on the largest payoff. 15) The maximum likelihood criterion ignores the payoffs for states of nature other than the most likely one. 16) The equally likely criterion assigns a probability of 0.5 to each state of nature. 17) Bayes' decision rule says to choose the alternative with the largest expected payoff. 18) Using Bayes' decision rule will always lead to larger payoffs. 19) Sensitivity analysis may be useful in decision analysis since prior probabilities may be inaccurate. 20) Graphical analysis can only be used in sensitivity analysis for those problems that have two decision alternatives. 1 Copyright © 2019 McGraw-Hill

21) The EVPI indicates an upper limit in the amount a decision-maker should be willing to spend to obtain information. 22) A posterior probability is a revised probability of a state of nature after doing a test or survey to refine the prior probability. 23) Bayes' theorem is a formula for determining prior probabilities of a state of nature. 24) A risk seeker has a decreasing marginal utility for money. 25) Utilities can be useful when monetary values do not accurately reflect the true values of an outcome. 26) Most people occupy a middle ground and are classified as risk neutral. 27) A utility function for money can be constructed by applying a lottery procedure. 28) The exponential utility function assumes a constant aversion to risk. 29) Two people who face the same problem and use the same decision-making methodology must always arrive at the same decision. 30) Which of the following is not a criterion for decision making? A) EVPI. B) Maximin C) Maximax D) Bayes' decision rule E) Maximum likelihood 31) Which one of the following statements is not correct when making decisions? A) The sum of the state of nature probabilities must be 1. B) Every probability must be greater than or equal to 0. C) All probabilities are assumed to be equal. D) Probabilities are used to compute expected values. E) Perfect information assumes that the state of nature that will actually occur is known. 32) Testing how a problem solution reacts to changes in one or more of the model parameters is called: A) analysis of tradeoffs. B) sensitivity analysis. C) priority recognition. D) analysis of variance. E) decision analysis.

33) Determining the worst payoff for each alternative and choosing the alternative with the "best worst" is the criterion called: A) minimin. B) maximin. C) maximax. D) maximum likelihood. E) Bayes decision rule. 34) The maximin criterion refers to: A) minimizing the maximum return. B) maximizing the minimum return. C) choosing the alternative with the highest payoff. D) choosing the alternative with the minimum payoff. E) None of the answer choices is correct. 35) Based on the following payoff table, answer the following: Alternative Buy Rent Lease Prior Probability

High Low 90 −10 70 40 60 55 0.4 0.6

The maximax strategy is: A) Buy. B) Rent. C) Lease. D) High. E) Low. 36) Based on the following payoff table, answer the following: Alternative Buy Rent Lease Prior Probability

High Low 90 −10 70 40 60 55 0.4 0.6

37) Based on the following payoff table, answer the following: Alternative

High Low 90 −10 70 40 60 55 0.4 0.6

Buy Rent Lease Prior Probability The maximum likelihood strategy is: A) Buy. B) Rent. C) Lease. D) High. E) Low.

38) Based on the following payoff table, answer the following: Alternative

High Low 90 −10 70 40 60 55 0.4 0.6

Buy Rent Lease Prior Probability The Bayes' decision rule strategy is: A) Buy. B) Rent. C) Lease. D) High. E) Low.

39) Based on the following payoff table, answer the following: Alternative

High Low 90 −10 70 40 60 55 0.4 0.6

Buy Rent Lease Prior Probability The expected value of perfect information is: A) 12. B) 55. C) 57. D) 69. E) 90.

40) Based on the following payoff table, answer the following: Alternative Small Medium Medium Large Large Extra Large Prior Probability

Yes

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The maximax strategy is: A) small. B) medium. C) medium large. D) large. E) extra large. 41) Based on the following payoff table, answer the following: Alternative Small Medium Medium Large Large Extra Large Prior Probability

Yes

10 20 30 40 60 0.3

The maximin strategy is: A) small. B) medium. C) medium large. D) large. E) extra large.

30 40 45 35 20 0.7

42) Based on the following payoff table, answer the following: Alternative

Yes

Small Medium Medium Large Large Extra Large Prior Probability

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The maximum likelihood strategy is: A) small. B) medium. C) medium large. D) large. E) extra large. 43) Based on the following payoff table, answer the following: Alternative

Yes

Small Medium Medium Large Large Extra Large Prior Probability

10 20 30 40 60 0.3

The Bayes' decision rule strategy is: A) small. B) medium. C) medium large. D) large. E) extra large.

30 40 45 35 20 0.7

44) Based on the following payoff table, answer the following: Alternative

Yes

Small Medium Medium Large Large Extra Large Prior Probability

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The expected value of perfect information is: A) 4.5. B) 9. C) 40.5. D) 49.5. E) 60. 45) Based on the following payoff table, answer the following: Alternative A B C D E Prior Probability

High

Medium 20 25 30 10 50 0.3

The maximax strategy is: A) A. B) B. C) C. D) D. E) E.

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

46) Based on the following payoff table, answer the following: Alternative

High

A B C D E Prior Probability

Medium 20 25 30 10 50 0.3

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

The maximin strategy is: A) A. B) B. C) C. D) D. E) E. 47) Based on the following payoff table, answer the following: Alternative

High

A B C D E Prior Probability

Medium 20 25 30 10 50 0.3

The maximum likelihood strategy is: A) A. B) B. C) C. D) D. E) E.

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

48) Based on the following payoff table, answer the following: Alternative

High

A B C D E Prior Probability

Medium 20 25 30 10 50 0.3

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

The Bayes' decision rule strategy is: A) A. B) B. C) C. D) D. E) E. 49) Based on the following payoff table, answer the following: Alternative

High

A B C D E Prior Probability

Medium 20 25 30 10 50 0.3

The expected value of perfect information is: A) −28. B) 0. C) 10.5. D) 19. E) 23.

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

50) The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.

Bus Small Medium Large Prior Probability

Low 50 40 20 0.3

Demand Medium 60 80 50 0.3

High 70 90 120 0.4

If he uses the maximum likelihood criterion, which size bus will he decide to purchase? A) Small B) Medium C) Large D) Either small or medium E) Either medium or large 51) The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.

Bus Small Medium Large Prior Probability

Low 50 40 20 0.3

Demand Medium 60 80 50 0.3

If he uses Bayes' decision rule, which size bus will he decide to purchase? A) Small B) Medium C) Large D) Either small or medium E) Either medium or large

High 70 90 120 0.4

52) The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.

Bus

Low 50 40 20 0.3

Small Medium Large Prior Probability

Demand Medium 60 80 50 0.3

High 70 90 120 0.4

What is the expected annual profit for the bus that he will decide to purchase using Bayes' decision rule? A) $15,000 B) $61,000 C) $69,000 D) $72,000 E) $87,000 53) The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.

Bus

Low 50 40 20 0.3

Small Medium Large Prior Probability What is his expected value of perfect information? A) $15,000 B) $61,000 C) $69,000 D) $72,000 E) $87,000

Demand Medium 60 80 50 0.3

High 70 90 120 0.4

54) The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

If he uses the maximum likelihood criterion, which kind of dwellings will he decide to build? A) Single family B) Apartments C) Condos D) Either single family or apartments E) Either apartments or condos 55) The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

If he uses Bayes' decision rule, which kind of dwellings will he decide to build? A) Single family B) Apartments C) Condos D) Either single family or apartments E) Either apartments or condos

56) The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

What is the expected annual profit for the dwellings that he will decide to build using Bayes' decision rule? A) $187,000 B) $132,000 C) $123,000 D) $65,000 E) $55,000 57) The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

What is his expected value of perfect information? A) $187,000 B) $132,000 C) $123,000 D) $65,000 E) $55,000

58) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What would be the total payoff is script #1 were a success, but its sequel were not? A) $150 million B) $100 million C) $90 million D) $50 million E) $−10 million 59) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the probability that script #1 will be a success, but its sequel will not? A) 0.8 B) 0.7 C) 0.56 D) 0.2 E) 0.14 60) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the expected payoff from selecting script #1? A) $150 million B) $90.6 million C) $84 million D) $72 million E) $60 million 14 Copyright © 2019 McGraw-Hill

61) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the expected payoff from selecting script #2? A) $150 million B) $90.6 million C) $84 million D) $72 million E) $60 million 62) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the expected payoff for the optimum decision alternative? A) $150 million B) $90.6 million C) $84 million D) $72 million E) $60 million 63) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the probability that the economics book would wind up being placed with a smaller publisher? A) 0.8 B) 0.5 C) 0.4 D) 0.2 E) 0.1 15 Copyright © 2019 McGraw-Hill

64) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the probability that the statistics book would wind up being placed with a smaller publisher? A) 0.6 B) 0.5 C) 0.4 D) 0.3 E) 0 65) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the expected payoff for the decision to write the economics book? A) 50,000 copies B) 40,000 copies C) 32,000 copies D) 30,500 copies E) 10,500 copies 66) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the expected payoff for the decision to write the statistics book? A) 50,000 copies B) 40,000 copies C) 32,000 copies D) 30,500 copies E) 10,500 copies 16 Copyright © 2019 McGraw-Hill

67) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the expected payoff for the optimum decision alternative? A) 50,000 copies B) 40,000 copies C) 32,000 copies D) 30,500 copies E) 10,500 copies 68) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

69) Refer to the following payoff table: State of Nature S1 S2 75 −40 0 100 0.6 0.4

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

71) Refer to the following payoff table: State of Nature S1 S2 75 −40 0 100 0.6 0.4

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

73) Refer to the following payoff table: State of Nature S1 S2 75 −40 0 100 0.6 0.4

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

75) Refer to the following payoff table: State of Nature S1 S2 75 −40 0 100 0.6 0.4

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

77) Refer to the following payoff table: State of Nature S1 S2 75 −40 0 100 0.6 0.4

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

79) A risk-averse decision maker is trying to decide which alternative to choose. The payoff table for the alternatives, given two possible states of nature, is shown below. Assuming that the decision makers risk tolerance (R) is 5, which decision should she choose based on the utility of each outcome? Assume the exponential utility function is applicable. Alternative A B C D E Prior Probability

High 20 25 30 10 50 0.3

Low 5 11 13 12 −28 0.7

A) Alternative A B) Alternative B C) Alternative C D) Alternative D E) Alternative E 80) What is the role of the group facilitator in decision conferencing? A) Lead the group to the desired outcome. B) Structure and focus discussions. C) Provide mathematical support for decision analysis. D) Determine the states of nature. E) Determine the payoffs for each alternative.

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 9 Decision Analysis 1) States of nature are alternatives available to a decision maker. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: The Goferbroke Company Problem Learning Objective: Describe the logical way in which decision analysis organizes a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) In decision analysis, states of nature refer to possible future conditions. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The Goferbroke Company Problem Learning Objective: Describe the logical way in which decision analysis organizes a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) Prior probabilities refer to the relative likelihood of possible states of nature. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The Goferbroke Company Problem Learning Objective: Describe the logical way in which decision analysis organizes a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) Payoffs always represent profits in decision analysis problems. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: The Goferbroke Company Problem Learning Objective: Describe the logical way in which decision analysis organizes a problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

5) A decision tree branches out all of the possible decisions and all of the possible events. Answer: TRUE Difficulty: 1 Easy Topic: Decision Trees Learning Objective: Formulate and solve a decision tree for dealing with a sequence of decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) An advantage of payoff tables compared to decision trees is that they permit us to analyze situations involving sequential decisions. Answer: FALSE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Formulate a payoff table from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) Payoff tables may include only non-negative numbers. Answer: FALSE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Formulate a payoff table from a description of the problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) A event node in a decision tree indicates that a decision needs to be made at that point. Answer: FALSE Difficulty: 1 Easy Topic: Decision Trees Learning Objective: Formulate and solve a decision tree for dealing with a sequence of decisions. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

9) The maximax approach is an optimistic strategy. Answer: TRUE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) An example of maximax decision making is a person buying lottery tickets in hopes of a very big payoff. Answer: TRUE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) The maximin approach involves choosing the alternative with the highest payoff. Answer: FALSE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) The maximin criterion is an optimistic criterion. Answer: FALSE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) The maximin approach involves choosing the alternative that has the "best worst" payoff. Answer: TRUE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) The maximum likelihood criterion says to focus on the largest payoff. Answer: FALSE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) The maximum likelihood criterion ignores the payoffs for states of nature other than the most likely one. Answer: TRUE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) The equally likely criterion assigns a probability of 0.5 to each state of nature. Answer: FALSE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

17) Bayes' decision rule says to choose the alternative with the largest expected payoff. Answer: TRUE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Apply Bayes' decision rule to solve a decision analysis problem. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) Using Bayes' decision rule will always lead to larger payoffs. Answer: FALSE Difficulty: 1 Easy Topic: Decision Criteria Learning Objective: Apply Bayes' decision rule to solve a decision analysis problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) Sensitivity analysis may be useful in decision analysis since prior probabilities may be inaccurate. Answer: TRUE Difficulty: 1 Easy Topic: Sensitivity Analysis With Decision Trees Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) Graphical analysis can only be used in sensitivity analysis for those problems that have two decision alternatives. Answer: FALSE Difficulty: 1 Easy Topic: Sensitivity Analysis With Decision Trees Learning Objective: Formulate and solve a decision tree for dealing with a sequence of decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

21) The EVPI indicates an upper limit in the amount a decision-maker should be willing to spend to obtain information. Answer: TRUE Difficulty: 1 Easy Topic: Checking Whether To Obtain More Information Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) A posterior probability is a revised probability of a state of nature after doing a test or survey to refine the prior probability. Answer: TRUE Difficulty: 1 Easy Topic: Using New Information To Update The Probabilities Learning Objective: Use new information to update the probabilities of the states of nature. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) Bayes' theorem is a formula for determining prior probabilities of a state of nature. Answer: FALSE Difficulty: 1 Easy Topic: Using New Information To Update The Probabilities Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 24) A risk seeker has a decreasing marginal utility for money. Answer: FALSE Difficulty: 1 Easy Topic: Using Utilities To Better Reflect The Values Of Payoffs Learning Objective: Use utilities to better reflect the values of payoffs. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

25) Utilities can be useful when monetary values do not accurately reflect the true values of an outcome. Answer: TRUE Difficulty: 1 Easy Topic: Using Utilities To Better Reflect The Values Of Payoffs Learning Objective: Use utilities to better reflect the values of payoffs. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) Most people occupy a middle ground and are classified as risk neutral. Answer: FALSE Difficulty: 1 Easy Topic: Using Utilities To Better Reflect The Values Of Payoffs Learning Objective: Use utilities to better reflect the values of payoffs. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) A utility function for money can be constructed by applying a lottery procedure. Answer: TRUE Difficulty: 1 Easy Topic: Using Utilities To Better Reflect The Values Of Payoffs Learning Objective: Use utilities to better reflect the values of payoffs. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) The exponential utility function assumes a constant aversion to risk. Answer: TRUE Difficulty: 1 Easy Topic: Using Utilities To Better Reflect The Values Of Payoffs Learning Objective: Use utilities to better reflect the values of payoffs. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

29) Two people who face the same problem and use the same decision-making methodology must always arrive at the same decision. Answer: FALSE Difficulty: 1 Easy Topic: Using Utilities To Better Reflect The Values Of Payoffs Learning Objective: Use utilities to better reflect the values of payoffs. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) Which of the following is not a criterion for decision making? A) EVPI. B) Maximin C) Maximax D) Bayes' decision rule E) Maximum likelihood Answer: A Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) Which one of the following statements is not correct when making decisions? A) The sum of the state of nature probabilities must be 1. B) Every probability must be greater than or equal to 0. C) All probabilities are assumed to be equal. D) Probabilities are used to compute expected values. E) Perfect information assumes that the state of nature that will actually occur is known. Answer: C Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe the logical way in which decision analysis organizes a problem. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

32) Testing how a problem solution reacts to changes in one or more of the model parameters is called: A) analysis of tradeoffs. B) sensitivity analysis. C) priority recognition. D) analysis of variance. E) decision analysis. Answer: B Difficulty: 2 Medium Topic: Sensitivity Analysis With Decision Trees Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 33) Determining the worst payoff for each alternative and choosing the alternative with the "best worst" is the criterion called: A) minimin. B) maximin. C) maximax. D) maximum likelihood. E) Bayes decision rule. Answer: B Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 34) The maximin criterion refers to: A) minimizing the maximum return. B) maximizing the minimum return. C) choosing the alternative with the highest payoff. D) choosing the alternative with the minimum payoff. E) None of the answer choices is correct. Answer: B Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 9 Copyright © 2019 McGraw-Hill

35) Based on the following payoff table, answer the following: Alternative Buy Rent Lease Prior Probability

High Low 90 −10 70 40 60 55 0.4 0.6

The maximax strategy is: A) Buy. B) Rent. C) Lease. D) High. E) Low. Answer: A Explanation: The maximax strategy chooses the alternative that has the highest maximum payoff. In this case, "Buy" has a maximum payoff of 90, which is the highest payoff in the table. Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

36) Based on the following payoff table, answer the following: Alternative Buy Rent Lease Prior Probability

High Low 90 −10 70 40 60 55 0.4 0.6

The maximin strategy is: A) Buy. B) Rent. C) Lease. D) High. E) Low. Answer: C Explanation: The maximin strategy chooses the alternative that has the highest minimum payoff. In this case, "Lease" has a minimum payoff of 55. Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

37) Based on the following payoff table, answer the following: Alternative

High Low 90 −10 70 40 60 55 0.4 0.6

Buy Rent Lease Prior Probability The maximum likelihood strategy is: A) Buy. B) Rent. C) Lease. D) High. E) Low.

Answer: C Explanation: The maximum likelihood strategy starts by identifying the most likely state of nature. In this case, the state of nature "Low" has the highest probability. Next, the strategy chooses the alternative that has the highest payoff for this state of nature. In this case, "Lease" has the highest payoff of 55 for the state of nature "Low." Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

38) Based on the following payoff table, answer the following: Alternative

High Low 90 −10 70 40 60 55 0.4 0.6

Buy Rent Lease Prior Probability The Bayes' decision rule strategy is: A) Buy. B) Rent. C) Lease. D) High. E) Low.

Answer: C Explanation: The Bayes' decision rule strategy begins with a calculation of the expected payoff for each alternative. The strategy then chooses the alternative with the highest expected payoff. Alternative Buy Rent Least

Expected Payoff 30 52 57

Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

39) Based on the following payoff table, answer the following: Alternative

High Low 90 −10 70 40 60 55 0.4 0.6

Buy Rent Lease Prior Probability The expected value of perfect information is: A) 12. B) 55. C) 57. D) 69. E) 90.

Answer: A Explanation: EVPI = EP(with perfect info) – EP(without more info). With perfect information, the payoff would be 90(0.4) + 55(0.6) = 69. Without more information, EP is determined using Bayes' decision rule (EP = 57). Therefore, EVPI = 69 − 57 = 12. Difficulty: 2 Medium Topic: Checking Whether To Obtain More Information Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

40) Based on the following payoff table, answer the following: Alternative Small Medium Medium Large Large Extra Large Prior Probability

Yes

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The maximax strategy is: A) small. B) medium. C) medium large. D) large. E) extra large. Answer: E Explanation: The maximax strategy chooses the alternative that has the highest maximum payoff. In this case, "Extra Large" has a maximum payoff of 90, which is the highest payoff in the table. Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

41) Based on the following payoff table, answer the following: Alternative Small Medium Medium Large Large Extra Large Prior Probability

Yes

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The maximin strategy is: A) small. B) medium. C) medium large. D) large. E) extra large. Answer: D Explanation: The maximin strategy chooses the alternative that has the highest minimum payoff. In this case, "Large" has a minimum payoff of 35. Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

42) Based on the following payoff table, answer the following: Alternative

Yes

Small Medium Medium Large Large Extra Large Prior Probability

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The maximum likelihood strategy is: A) small. B) medium. C) medium large. D) large. E) extra large. Answer: C Explanation: The maximum likelihood strategy starts by identifying the most likely state of nature. In this case, the state of nature "No" has the highest probability. Next, the strategy chooses the alternative that has the highest payoff for this state of nature. In this case, "Medium Large" has the highest payoff of 45 for the state of nature "No." Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

43) Based on the following payoff table, answer the following: Alternative

Yes

Small Medium Medium Large Large Extra Large Prior Probability

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The Bayes' decision rule strategy is: A) small. B) medium. C) medium large. D) large. E) extra large. Answer: C Explanation: The Bayes' decision rule strategy begins with a calculation of the expected payoff for each alternative. The strategy then chooses the alternative with the highest expected payoff. Alternative Small Medium Medium Large Large Extra Large

Expected Payoff 24 34 40.5 36.5 32

Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

44) Based on the following payoff table, answer the following: Alternative

Yes

Small Medium Medium Large Large Extra Large Prior Probability

10 20 30 40 60 0.3

30 40 45 35 20 0.7

The expected value of perfect information is: A) 4.5. B) 9. C) 40.5. D) 49.5. E) 60. Answer: B Explanation: EVPI = EP (with perfect info) − EP (without more info). With perfect information, the payoff would be 60(0.3) + 45(0.7) = 49.5. Without more information, EP is determined using Bayes' decision rule (EP = 40.5). Therefore, EVPI = 49.5 − 40.5 = 9. Difficulty: 3 Hard Topic: Checking Whether To Obtain More Information Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

45) Based on the following payoff table, answer the following: Alternative A B C D E Prior Probability

High

Medium 20 25 30 10 50 0.3

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

The maximax strategy is: A) A. B) B. C) C. D) D. E) E. Answer: E Explanation: The maximax strategy chooses the alternative that has the highest maximum payoff. In this case, "E" has a maximum payoff of 50, which is the highest payoff in the table. Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

46) Based on the following payoff table, answer the following: Alternative A B C D E Prior Probability

High

Medium 20 25 30 10 50 0.3

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

The maximin strategy is: A) A. B) B. C) C. D) D. E) E. Answer: C Explanation: The maximin strategy chooses the alternative that has the highest minimum payoff. In this case, "C" has a minimum payoff of 13. Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

47) Based on the following payoff table, answer the following: Alternative

High

A B C D E Prior Probability

Medium 20 25 30 10 50 0.3

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

The maximum likelihood strategy is: A) A. B) B. C) C. D) D. E) E. Answer: C Explanation: The maximum likelihood strategy starts by identifying the most likely state of nature. In this case, the state of nature "Low" has the highest probability. Next, the strategy chooses the alternative that has the highest payoff for this state of nature. In this case, "C" has the highest payoff of 13 for the state of nature "Low." Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

48) Based on the following payoff table, answer the following: Alternative

High

A B C D E Prior Probability

Medium 20 25 30 10 50 0.3

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

The Bayes' decision rule strategy is: A) A. B) B. C) C. D) D. E) E. Answer: B Explanation: The Bayes' decision rule strategy begins with a calculation of the expected payoff for each alternative. The strategy then chooses the alternative with the highest expected payoff. Alternative A B C D E

Expected Payoff 12.5 19 17.9 11.4 9

Difficulty: 3 Hard Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

49) Based on the following payoff table, answer the following: Alternative

High

A B C D E Prior Probability

Medium 20 25 30 10 50 0.3

Low 20 30 12 12 40 0.2

5 11 13 12 −28 0.5

The expected value of perfect information is: A) −28. B) 0. C) 10.5. D) 19. E) 23. Answer: C Explanation: EVPI = EP(with perfect info) − EP(without more info). With perfect information, the payoff would be 50(0.3) + 40(0.2) + 13(0.5) = 29.5. Without more information, EP is determined using Bayes' decision rule (EP = 19). Therefore, EVPI = 29.5 − 19 = 10.5. Difficulty: 3 Hard Topic: Checking Whether To Obtain More Information Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Bus Small Medium Large Prior Probability

Low 50 40 20 0.3

Demand Medium 60 80 50 0.3

High 70 90 120 0.4

If he uses the maximum likelihood criterion, which size bus will he decide to purchase? A) Small B) Medium C) Large D) Either small or medium E) Either medium or large Answer: C Explanation: The maximum likelihood strategy starts by identifying the most likely state of nature. In this case, the state of nature "High" has the highest probability. Next, the strategy chooses the alternative that has the highest payoff for this state of nature. In this case, "Large" has the highest payoff of 120 for the state of nature "High." Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

51) The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.

Bus

Low 50 40 20 0.3

Small Medium Large Prior Probability

Demand Medium 60 80 50 0.3

High 70 90 120 0.4

If he uses Bayes' decision rule, which size bus will he decide to purchase? A) Small B) Medium C) Large D) Either small or medium E) Either medium or large Answer: B Explanation: The Bayes' decision rule strategy begins with a calculation of the expected payoff for each alternative. The strategy then chooses the alternative with the highest expected payoff. Alternative Small Medium Large

Expected Payoff 61,000 72,000* 69,000

Bus

Low 50 40 20 0.3

Small Medium Large Prior Probability

Demand Medium 60 80 50 0.3

High 70 90 120 0.4

What is the expected annual profit for the bus that he will decide to purchase using Bayes' decision rule? A) $15,000 B) $61,000 C) $69,000 D) $72,000 E) $87,000 Answer: D Explanation: The Bayes' decision rule strategy begins with a calculation of the expected payoff for each alternative. The strategy then chooses the alternative with the highest expected payoff. Alternative Small Medium Large

Expected Payoff 61,000 72,000 69,000

53) The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.

Bus

Low 50 40 20 0.3

Small Medium Large Prior Probability

Demand Medium 60 80 50 0.3

High 70 90 120 0.4

What is his expected value of perfect information? A) $15,000 B) $61,000 C) $69,000 D) $72,000 E) $87,000 Answer: A Explanation: EVPI = EP (with perfect info) − EP (without more info). With perfect information, the payoff would be 50,000(0.3) + 80,000(0.3) + 120,000(0.4) = 87,000. Without more information, EP is determined using Bayes' decision rule (EP = 72,000). Therefore, EVPI = 87,000 − 72,000 = 15,000. Difficulty: 3 Hard Topic: Checking Whether To Obtain More Information Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

If he uses the maximum likelihood criterion, which kind of dwellings will he decide to build? A) Single family B) Apartments C) Condos D) Either single family or apartments E) Either apartments or condos Answer: B Explanation: The maximum likelihood strategy starts by identifying the most likely state of nature. In this case, the state of nature "Stable" has the highest probability. Next, the strategy chooses the alternative that has the highest payoff for this state of nature. In this case, "Apartments" has the highest payoff of 170 for the state of nature "Stable." Difficulty: 2 Medium Topic: Decision Criteria Learning Objective: Describe and evaluate several alternative criteria for making a decision based on a payoff table. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

55) The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

If he uses Bayes' decision rule, which kind of dwellings will he decide to build? A) Single family B) Apartments C) Condos D) Either single family or apartments E) Either apartments or condos Answer: A Explanation: The Bayes' decision rule strategy begins with a calculation of the expected payoff for each alternative. The strategy then chooses the alternative with the highest expected payoff. Alternative Single Family Apartments Condos

Expected Payoff 132,000 122,000 64,000

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

What is the expected annual profit for the dwellings that he will decide to build using Bayes' decision rule? A) $187,000 B) $132,000 C) $123,000 D) $65,000 E) $55,000 Answer: B Explanation: The Bayes' decision rule strategy begins with a calculation of the expected payoff for each alternative. The strategy then chooses the alternative with the highest expected payoff. Alternative Single Family Apartments Condos

Expected Payoff 132,000 122,000 64,000

57) The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

Type Single Family Apartments Condos Prior Probability

Population Trend Declining Stable Growing 200 90 70 70 170 90 −20 100 220 0.4 0.5 0.1

What is his expected value of perfect information? A) $187,000 B) $132,000 C) $123,000 D) $65,000 E) $55,000 Answer: E Explanation: EVPI = EP (with perfect info) − EP (without more info). With perfect information, the payoff would be 200,000(0.4) + 170,000(0.5) + 220,000(0.1) = 187,000. Without more information, EP is determined using Bayes' decision rule (EP = 132,000). Therefore, EVPI = 187,000 − 132,000 = 55,000. Difficulty: 3 Hard Topic: Checking Whether To Obtain More Information Learning Objective: Perform sensitivity analysis with Bayes' decision rule. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

59) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the probability that script #1 will be a success, but its sequel will not? A) 0.8 B) 0.7 C) 0.56 D) 0.2 E) 0.14 Answer: E Explanation: The probability of a sequence of events is the product of the individual probabilities. Success of script #1 (0.7) × Failure of sequel (0.2) = 0.14. Difficulty: 2 Medium Topic: Decision Trees Learning Objective: Formulate and solve a decision tree for dealing with a sequence of decisions. Bloom's: Analyze AACSB: Knowledge Application Accessibility: Keyboard Navigation

60) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the expected payoff from selecting script #1? A) $150 million B) $90.6 million C) $84 million D) $72 million E) $60 million Answer: B Explanation: The expected payoff is the weighted average of the individual payoffs. This problem is best analyzed with a decision tree (shown below). The expected payoff is $90.6 million.

Difficulty: 3 Hard Topic: Decision Trees Learning Objective: Formulate and solve a decision tree for dealing with a sequence of decisions. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

62) The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. She feels that script #1 has a 70% chance of earning $100 million over the long run, but a 30% chance of losing $20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning $50 million, but a 20% chance of losing $10 million. On the other hand, she feels that script #2 has a 60 % chance of earning $120 million, but a 40% chance of losing $30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the expected payoff for the optimum decision alternative? A) $150 million B) $90.6 million C) $84 million D) $72 million E) $60 million Answer: B Explanation: The expected payoff is the weighted average of the individual payoffs. This problem is best analyzed with a decision tree (shown below). The optimal decision is to pursue script #1 and the expected payoff is $90.6 million.

63) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the probability that the economics book would wind up being placed with a smaller publisher? A) 0.8 B) 0.5 C) 0.4 D) 0.2 E) 0.1 Answer: C Explanation: Being placed with a small publisher requires two events to occur. First, the book must be rejected by the large publisher (probability 0.5) and then the book must be accepted by the small publisher (probability 0.8). The probability of these two events occurring is the product of their individual probabilities (0.5 × 0.8 = 0.4). Difficulty: 2 Medium Topic: Decision Trees Learning Objective: Formulate and solve a decision tree for dealing with a sequence of decisions. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

65) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the expected payoff for the decision to write the economics book? A) 50,000 copies B) 40,000 copies C) 32,000 copies D) 30,500 copies E) 10,500 copies Answer: C Explanation: The expected payoff is the weighted average of the individual payoffs. This problem is best analyzed with a decision tree (shown below). The expected payoff is 32,000 copies.

66) Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand if they write a statistics book, they feel they have a 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the expected payoff for the decision to write the statistics book? A) 50,000 copies B) 40,000 copies C) 32,000 copies D) 30,500 copies E) 10,500 copies Answer: D Explanation: The expected payoff is the weighted average of the individual payoffs. This problem is best analyzed with a decision tree (shown below). The expected payoff is 30,500 copies.

68) Refer to the following payoff table: State of Nature S1 S2 75 −40 0 100 0.6 0.4

Alternative A1 A2 Prior Probability

Expected Payoff 29 40

69) Refer to the following payoff table: State of Nature S1 S2 75 −40 0 100 0.6 0.4

Alternative A1 A2 Prior Probability

70) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. Given that the research is done, what is the joint probability that the state of nature is S1 and the research predicts S1? A) 0.08 B) 0.16 C) 0.24 D) 0.32 E) 0.36 Answer: E Explanation: The prior probability of state S1 is 0.6. Since the probability that the research will predict S1 when S1 is the true case is also 0.6, the joint probability is the product of the two individual probabilities (0.6 × 0.6 = 0.36). Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

71) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. Given that the research is done, what is the joint probability that the state of nature is S1 and the research predicts S2? A) 0.08 B) 0.16 C) 0.24 D) 0.32 E) 0.36 Answer: C Explanation: The prior probability of state S1 is 0.6. Since the probability that the research will predict S1 when S1 is the true case is 0.6, the probability that the research will predict S2 is 1 − 0.6 = 0.4. The joint probability is the product of the two individual probabilities (0.6 × 0.4 = 0.24). Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

72) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. Given that the research is done, what is the joint probability that the state of nature is S2 and the research predicts S1? A) 0.08 B) 0.16 C) 0.24 D) 0.32 E) 0.36 Answer: A Explanation: The prior probability of state S2 is 0.4. Since the probability that the research will predict S2 when S2 is the true case is 0.8, the probability that the research will predict S1 is 1 − 0.8 = 0.2. The joint probability is the product of the two individual probabilities (0.4 × 0.2 = 0.08). Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

73) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. Given that the research is done, what is the joint probability that the state of nature is S2 and the research predicts S2? A) 0.08 B) 0.16 C) 0.24 D) 0.32 E) 0.36 Answer: D Explanation: The prior probability of state S2 is 0.4. Since the probability that the research will predict S2 when S2 is the true case is 0.8, the joint probability is the product of the two individual probabilities (0.4 × 0.8 = 0.32). Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

74) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. What is the unconditional probability that the research predicts S1? A) 0.32 B) 0.4 C) 0.44 D) 0.56 E) 0.6 Answer: C Explanation: The prior probability of state S1 is 0.6. Since the probability that the research will predict S1 when S1 is the true case is also 0.6, the joint probability of correctly predicting S1 is the product of the two individual probabilities (0.6 × 0.6 = 0.36). The prior probability of state S2 is 0.4. Since the probability that the research will predict S2 when S2 is the true case is 0.8, the probability that the research will predict S1 is 1 − 0.8 = 0.2. The joint probability or incorrectly predicting S1 is the product of the two individual probabilities (0.4 × 0.2 = 0.08). The unconditional probability of predicting S1 is the sum of the two joint probabilities (0.36 + 0.08 = 0.44). Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

75) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. What is the unconditional probability that the research predicts S2? A) 0.32 B) 0.4 C) 0.44 D) 0.56 E) 0.6 Answer: D Explanation: The prior probability of state S1 is 0.6. Since the probability that the research will predict S2 when S1 is the true case is 0.4, the joint probability of incorrectly predicting S2 is the product of the two individual probabilities (0.6 × 0.4 = 0.24). The prior probability of state S2 is 0.4. Since the probability that the research will predict S2 when S2 is the true case is 0.8, the joint probability or correctly predicting S2 is the product of the two individual probabilities (0.4 × 0.8 = 0.32). The unconditional probability of predicting S1 is the sum of the two joint probabilities (0.24 + 0.32 = 0.56). Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

76) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. What is the posterior probability of S1 given that the research predicts S1? A) 0.18 B) 0.44 C) 0.57 D) 0.65 E) 0.82 Answer: E Explanation: The prior probability of state S1 is 0.6. The probability of the research predicting S1 is the probability of correctly predicting S1 (0.6 × 0.6 = 0.36) plus the probability of incorrectly predicting S1 (0.2 × 0.4 = 0.08) for a total of 0.44. Thus, the posterior probability that the true state is S1 given a prediction of S1 is . Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

77) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

. Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Determine whether it is worthwhile to obtain more information before making a decision. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

78) Refer to the following payoff table:

Alternative A1 A2 Prior Probability

State of Nature S1 S2 75 −40 0 100 0.6 0.4

Answer: B Explanation: This problem is best analyzed with a decision tree. The expected payoff when the research is done is −44.

Difficulty: 3 Hard Topic: Using New Information To Update The Probabilities Learning Objective: Use new information to update the probabilities of the states of nature. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

High 20 25 30 10 50 0.3

Low 5 11 13 12 −28 0.7

A) Alternative A B) Alternative B C) Alternative C D) Alternative D E) Alternative E Answer: C Explanation: First, convert the monetary payoffs to utilities using the exponential utility function , then calculate uses Bayes' decision rule to choose the alternative with the highest expected utility (Alternative C). The utility table and expected utilities are shown below: Alternative A B C D E Prior Probabilities

Utility High Utility Low Expected Utility 0.982 0.632 0.737 0.993 0.889 0.920 0.998 0.926 0.947* 0.865 0.909 0.896 1.000 −269.426 −188.298 0.3 0.7

Difficulty: 3 Hard Topic: Using Utilities To Better Reflect The Values Of Payoffs Learning Objective: Use utilities to better reflect the values of payoffs. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

80) What is the role of the group facilitator in decision conferencing? A) Lead the group to the desired outcome. B) Structure and focus discussions. C) Provide mathematical support for decision analysis. D) Determine the states of nature. E) Determine the payoffs for each alternative. Answer: B Difficulty: 1 Easy Topic: The Practical Application Of Decision Analysis Learning Objective: Describe some common features in the practical application of decision analysis. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 10 Forecasting 1) Forecasts are rarely perfect. 2) Once accepted by managers, forecasts should not be overridden. 3) When no historical sales data is available, it is best to use statistical forecasting methods. 4) The difference between a forecast and what turns out to be the true value is called the mean absolute deviation. 5) The mean absolute deviation is the sum of the absolute value of forecasting errors divided by the number of forecasts. 6) The mean square error is the square of the mean of the absolute deviations. 7) The mean absolute deviation is more sensitive to large deviations than the mean square error. 8) The seasonal factor for any period of a year measures how that period compares to the same period last year. 9) Removing the seasonal component from a time-series can be accomplished by dividing each value by its appropriate seasonal factor. 10) The last-value forecasting method requires a linear trend line. 11) The last-value forecasting method is most useful when conditions are stable over time. 12) The averaging method uses all the data points in the time-series. 13) A moving-average forecast tends to be more responsive to changes in the time-series data when more values are included in the average. 14) The moving-average forecasting method assigns equal weights to each value that is represented by the average. 15) The moving-average forecasting method is a very good one when conditions remain pretty much the same over the time period being considered. 16) An advantage of the exponential smoothing forecasting method is that more recent experience is given more weight than less recent experience. 17) A smoothing constant of 0.1 will cause an exponential smoothing forecast to react more quickly to a sudden change than a value of 0.3 will. 18) If significant changes in conditions are occurring relatively frequently, then a smaller smoothing constant is needed. 1 Copyright © 2019 McGraw-Hill

19) Exponential smoothing with trend requires selection of two smoothing constants. 20) Exponential smoothing with trend was designed for time-series that have great variability both up and down. 21) Forecasting techniques such as moving-average, exponential smoothing, and the last-value method all represent averaged values of time-series data. 22) In exponential smoothing, an α of 0.3 will cause a forecast to react more quickly to a large error than will an α of 0.2. 23) The goal of time-series forecasting methods is to estimate the mean of the underlying probability distribution of the next value of the time-series as closely as possible. 24) If a time-series has exactly the same distribution for each and every time period, then the averaging forecasting method provides the best estimate of the mean. 25) A time-series is said to be smooth if its underlying probability distribution usually remains the same from one period to the next. 26) Causal forecasting obtains a forecast for a dependent variable by relating it directly to one or more independent variables. 27) Linear regression can be used to approximate the relationship between independent and dependent variables. 28) Judgmental forecasting methods have been developed to interpret statistical data. 29) The sales force composite method is a top-down approach to forecasting. 30) The Delphi method involves the use of a series of questionnaires to achieve a consensus forecast. 31) When statistical forecasting methods are used, it is no longer necessary to use judgmental methods as well. 32) Forecasts can help a manager to: A) anticipate the future. B) develop strategies. C) make staffing decisions. D) All of the answers choices are correct. E) None of the answer choices is correct.

33) In business, forecasts are the basis for: A) sales planning. B) inventory planning. C) production planning. D) budgeting. E) All of the answers choices are correct. 34) Which of the following are costs of an inaccurate forecast? A) Lost sales B) Inventory C) An understaffed office D) Lower profits E) All of the answers choices are correct. 35) Time-series data may exhibit which of the following behaviors? A) Trend B) Seasonality C) Cycles D) Irregularities E) All of the answers choices are correct 36) Gradual, long-term movement in time-series values is called: A) seasonal variation. B) trend. C) cycles. D) irregular variation. E) random variation. 37) The last-value forecasting method: A) is quick and easy to prepare. B) is easy for users to understand. C) ignores all values except one. D) All of the answers choices are correct. E) None of the answer choices is correct. 38) Using the latest value in a sequence of data to forecast the next period is: A) a moving-average forecast. B) a last-value forecast. C) an exponentially smoothed forecast. D) a causal forecast. E) None of the answer choices is correct.

39) Refer to the following data: Period 1 2 3 4

Demand 58 59 60 61

What is the last-value forecast for the next period? A) 58 B) 62 C) 60 D) 61 E) None of the answer choices is correct. 40) Refer to the following data: Period 1 2 3 4

Demand 58 59 60 61

What is the moving-average forecast for the next period based on the last three periods? A) 58 B) 62 C) 60 D) 61 E) None of the answer choices is correct. 41) In order to increase the responsiveness of a forecast made using the moving-average method, the number of values in the average should be: A) decreased. B) increased. C) multiplied by a larger α. D) multiplied by a smaller α. E) None of the answer choices is correct. 42) Which of the following smoothing constants would make an exponential smoothing forecast equivalent to a last-value forecast? A) 0 B) 0.01 C) 0.1 D) 0.5 E) 1 4 Copyright © 2019 McGraw-Hill

43) Given an actual latest demand of 59, a previous forecast of 64, and α = 0.3, what would be the forecast for the next period using the exponential smoothing method? A) 36.9 B) 57.5 C) 60.5 D) 62.5 E) 65.5 44) Given an actual latest demand of 105, a previous forecast of 97, and α = 0.4, what would be the forecast for the next period using the exponential smoothing method? A) 80.8 B) 93.8 C) 100.2 D) 101.8 E) 108.2 45) Which of the following possible values of α would cause exponential smoothing to respond the most quickly to forecast errors? A) 0 B) 0.01 C) 0.05 D) 0.1 E) 0.15 46) In exponential smoothing with trend, the forecast consists of: A) an exponentially smoothed forecast and a smoothed trend factor. B) the old forecast adjusted by a trend factor. C) the old forecast and a smoothed trend factor. D) a moving-average and a trend factor. E) None of the answer choices is correct. 47) The mean absolute deviation is used to: A) estimate the trend line. B) eliminate forecast errors. C) measure forecast accuracy. D) seasonally adjust the forecast. E) All of the answers choices are correct. 48) Given forecast errors of 4, 8, and −3, what is the mean absolute deviation? A) 3 B) 4 C) 5 D) 6 E) 9

49) Given forecast errors of 4, 8, and −3, what is the mean square error? A) 5 B) 9 C) 25 D) 29.67 E) 89 50) Given forecast errors of 5, 0, −4, and 3, what is the mean absolute deviation? A) 1 B) 2 C) 2.5 D) 3 E) 12 51) Given forecast errors of 5, 0, −4, and 3, what is the mean square error? A) 3 B) 4 C) 12 D) 12.5 E) 50 52) Given the following historical data, what is the moving-average forecast for period 6 based on the last three periods? Period 1 2 3 4 5

Value 73 68 65 72 67

A) 67 B) 68 C) 69 D) 100 E) 115

53) Given the following historical data, what is the moving-average forecast for period 6 based on the last three periods? Period 1 2 3 4 5

Value 19 20 18 19 17

A) 17 B) 18 C) 19 D) 20 E) 18.5 54) Given forecast errors of −5, -10, and 15, what is the mean absolute deviation? A) 0 B) 5 C) 10 D) 30 E) None of the answer choices is correct. 55) The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year 5 years ago 4 years ago 3 years ago 2 years ago Last year

Enrollments 15,000 16,000 18,000 20,000 21,000

What is the forecast for this year using the last-value forecasting method? A) 18,750 B) 19,500 C) 21,000 D) 22,650 E) 22,800

56) The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year 5 years ago 4 years ago 3 years ago 2 years ago Last year

Enrollments 15,000 16,000 18,000 20,000 21,000

What is the forecast for this year using a moving-average forecast based on the last four years? A) 18,750 B) 19,500 C) 21,000 D) 22,650 E) 22,800 57) The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year 5 years ago 4 years ago 3 years ago 2 years ago Last year

Enrollments 15,000 16,000 18,000 20,000 21,000

What is the forecast for this year using exponential smoothing with α = 0.5, if the forecast for two years ago was 16,000? A) 18,750 B) 19,500 C) 21,000 D) 22,650 E) 22,800

58) The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year 5 years ago 4 years ago 3 years ago 2 years ago Last year

Enrollments 15,000 16,000 18,000 20,000 21,000

Demand 900 700 600 500 300

What is the forecast for this year using the last-value forecasting method? A) 163 B) 180 C) 300 D) 467 E) 510

60) The business analyst for Ace Business Machines, Inc. wants to forecast this year's demand for manual typewriters based on the following historical data: Time Period 5 years ago 4 years ago 3 years ago 2 years ago Last year

Demand 900 700 600 500 300

What is the forecast for this year using a moving-average forecast based on the last three years? A) 163 B) 180 C) 300 D) 467 E) 510 61) The business analyst for Ace Business Machines, Inc. wants to forecast this year's demand for manual typewriters based on the following historical data: Time Period 5 years ago 4 years ago 3 years ago 2 years ago Last year

Demand 900 700 600 500 300

What is the forecast for this year using exponential smoothing with α = 0.4, if the forecast for two years ago was 750? A) 163 B) 180 C) 300 D) 467 E) 510

62) Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data: Week 6 weeks ago 5 weeks ago 4 weeks ago 3 weeks ago 2 weeks ago Last week

# of students 83 110 95 80 65 50

What is the forecast for this year using the last-value forecasting method? A) 49 B) 50 C) 52 D) 65 E) 78 63) Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data: Week 6 weeks ago 5 weeks ago 4 weeks ago 3 weeks ago 2 weeks ago Last week

# of students 83 110 95 80 65 50

What is the forecast for this year using a moving-average forecast based on the last three weeks? A) 49 B) 50 C) 52 D) 65 E) 78

64) Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data: Week 6 weeks ago 5 weeks ago 4 weeks ago 3 weeks ago 2 weeks ago Last week

# of students 83 110 95 80 65 50

What is the forecast for this year using exponential smoothing with α = 0.2, if the forecast for two weeks ago was 90? A) 49 B) 50 C) 52 D) 65 E) 78 65) Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data: Week 6 weeks ago 5 weeks ago 4 weeks ago 3 weeks ago 2 weeks ago Last week

# of students 83 110 95 80 65 50

66) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

What is the forecast for this year using the last-value forecasting method? A) 22,000 B) 20,000 C) 18,000 D) 15,000 E) 12,000 67) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

What is the forecast for this year using a moving-average forecast based on the last four years? A) 22,000 B) 20,000 C) 18,000 D) 15,000 E) 12,000

68) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

What is the forecast for this year using exponential smoothing with α = 0.2, if the forecast for last year was 15,000? A) 20,000 B) 19,000 C) 17,500 D) 16,000 E) 15,000 69) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

The previous trend line has predicted 18,500 for two years ago, and 19,700 for last year. What was the mean absolute deviation for these forecasts? A) 100 B) 200 C) 400 D) 500 E) 800 70) A manager uses the equation y = 40,000 + 150x to predict monthly receipts. What is the forecast for July if x = 0 in April? A) 40,450 B) 40,600 C) 42,100 D) 42,250 E) 42,400

71) The equation y = 350 − 2.5x is used to predict quarterly demand where x = 0 in the second quarter of last year. Quarterly seasonal factors are Q1 = 1.5, Q2 = 0.8, Q3 = 1.1, and Q4 = 0.6. What is the forecast for the last quarter of this year? A) 199.5 B) 201 C) 266 D) 268 E) 335 72) The primary method for causal forecasting is: A) sensitivity analysis. B) linear regression. C) moving-average. D) exponential smoothing. E) the Delphi method. 73) Which of the following is not a type of judgmental forecasting? A) Managerial opinion B) Sales force composite C) Time-series analysis D) The Delphi method E) Consumer market survey 74) Which of the following would be considered a possible drawback of using executive opinions to develop a forecast? A) It is difficult to interpret the results. B) Responsibility is diffused for the forecast. C) Extensive use of computers is needed. D) It brings together the knowledge of top managers. E) Forecasters are sometimes overly influenced by recent events. 75) Which of the following would be an advantage of using a sales force composite to develop a demand forecast? A) The sales staff is least affected by changing customer needs. B) The sales force can easily distinguish between customer desires and probable actions. C) The sales staff is often aware of customer's future plans. D) Salespeople are least likely to be biased by sales quotas. E) None of the answer choices is correct. 76) The forecasting method which uses anonymous questionnaires to achieve a consensus forecast is: A) sales force composites. B) consumer surveys. C) the Delphi method. D) time-series analysis. E) executive opinions.

77) The following table shows the quarterly sales of widgets over the past two years. Calculate the seasonal factor for Quarter 2. Quarter Q1 last year Q2 last year Q3 last year Q4 last year Q1 this year Q2 this year Q3 this year Q4 this year

Sales 10,000 11,000 7,500 8,000 15,000 17,000 10,500 11,500

A) 0.74 B) 0.99 C) 1.14 D) 1.24 E) 1.29

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 10 Forecasting 1) Forecasts are rarely perfect. Answer: TRUE Difficulty: 1 Easy Topic: An Overview of Forecasting Techniques Learning Objective: Describe some important types of forecasting applications. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) Once accepted by managers, forecasts should not be overridden. Answer: FALSE Difficulty: 1 Easy Topic: An Overview of Forecasting Techniques Learning Objective: Describe some important types of forecasting applications. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) When no historical sales data is available, it is best to use statistical forecasting methods. Answer: FALSE Difficulty: 2 Medium Topic: An Overview of Forecasting Techniques Learning Objective: Describe some important types of forecasting applications. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) The difference between a forecast and what turns out to be the true value is called the mean absolute deviation. Answer: FALSE Difficulty: 1 Easy Topic: An Overview of Forecasting Techniques Learning Objective: Identify two common measures of the accuracy of forecasting methods. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

5) The mean absolute deviation is the sum of the absolute value of forecasting errors divided by the number of forecasts. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: The Computer Club Warehouse (CCW) Problem Learning Objective: Identify two common measures of the accuracy of forecasting methods. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) The mean square error is the square of the mean of the absolute deviations. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: The Computer Club Warehouse (CCW) Problem Learning Objective: Identify two common measures of the accuracy of forecasting methods. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) The mean absolute deviation is more sensitive to large deviations than the mean square error. Answer: FALSE Difficulty: 2 Medium Topic: A Case Study: The Computer Club Warehouse (CCW) Problem Learning Objective: Identify two common measures of the accuracy of forecasting methods. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) The seasonal factor for any period of a year measures how that period compares to the same period last year. Answer: FALSE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Adjust forecasting data to consider seasonal patterns. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

9) Removing the seasonal component from a time-series can be accomplished by dividing each value by its appropriate seasonal factor. Answer: TRUE Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Adjust forecasting data to consider seasonal patterns. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) The last-value forecasting method requires a linear trend line. Answer: FALSE Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) The last-value forecasting method is most useful when conditions are stable over time. Answer: FALSE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) The averaging method uses all the data points in the time-series. Answer: TRUE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) A moving-average forecast tends to be more responsive to changes in the time-series data when more values are included in the average. Answer: FALSE Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) The moving-average forecasting method assigns equal weights to each value that is represented by the average. Answer: TRUE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) The moving-average forecasting method is a very good one when conditions remain pretty much the same over the time period being considered. Answer: TRUE Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) An advantage of the exponential smoothing forecasting method is that more recent experience is given more weight than less recent experience. Answer: TRUE Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 4 Copyright © 2019 McGraw-Hill

17) A smoothing constant of 0.1 will cause an exponential smoothing forecast to react more quickly to a sudden change than a value of 0.3 will. Answer: FALSE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) If significant changes in conditions are occurring relatively frequently, then a smaller smoothing constant is needed. Answer: FALSE Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) Exponential smoothing with trend requires selection of two smoothing constants. Answer: TRUE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) Exponential smoothing with trend was designed for time-series that have great variability both up and down. Answer: FALSE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

21) Forecasting techniques such as moving-average, exponential smoothing, and the last-value method all represent averaged values of time-series data. Answer: FALSE Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) In exponential smoothing, an α of 0.3 will cause a forecast to react more quickly to a large error than will an α of 0.2. Answer: TRUE Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) The goal of time-series forecasting methods is to estimate the mean of the underlying probability distribution of the next value of the time-series as closely as possible. Answer: TRUE Difficulty: 2 Medium Topic: The Time-Series Forecasting Methods in Perspective Learning Objective: Compare these methods to identify the conditions when each is particularly suitable. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 24) If a time-series has exactly the same distribution for each and every time period, then the averaging forecasting method provides the best estimate of the mean. Answer: TRUE Difficulty: 2 Medium Topic: The Time-Series Forecasting Methods in Perspective Learning Objective: Compare these methods to identify the conditions when each is particularly suitable. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 6 Copyright © 2019 McGraw-Hill

25) A time-series is said to be smooth if its underlying probability distribution usually remains the same from one period to the next. Answer: FALSE Difficulty: 1 Easy Topic: The Time-Series Forecasting Methods in Perspective Learning Objective: Compare these methods to identify the conditions when each is particularly suitable. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) Causal forecasting obtains a forecast for a dependent variable by relating it directly to one or more independent variables. Answer: TRUE Difficulty: 1 Easy Topic: Causal Forecasting With Linear Regression Learning Objective: Describe and apply an approach to forecasting that relates the quantity of interest to one or more other quantities. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) Linear regression can be used to approximate the relationship between independent and dependent variables. Answer: TRUE Difficulty: 1 Easy Topic: Causal Forecasting With Linear Regression Learning Objective: Describe and apply an approach to forecasting that relates the quantity of interest to one or more other quantities. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) Judgmental forecasting methods have been developed to interpret statistical data. Answer: FALSE Difficulty: 1 Easy Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

29) The sales force composite method is a top-down approach to forecasting. Answer: FALSE Difficulty: 2 Medium Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) The Delphi method involves the use of a series of questionnaires to achieve a consensus forecast. Answer: TRUE Difficulty: 1 Easy Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) When statistical forecasting methods are used, it is no longer necessary to use judgmental methods as well. Answer: FALSE Difficulty: 1 Easy Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 32) Forecasts can help a manager to: A) anticipate the future. B) develop strategies. C) make staffing decisions. D) All of the answers choices are correct. E) None of the answer choices is correct. Answer: D Difficulty: 2 Medium Topic: An Overview of Forecasting Techniques Learning Objective: Describe some important types of forecasting applications. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

33) In business, forecasts are the basis for: A) sales planning. B) inventory planning. C) production planning. D) budgeting. E) All of the answers choices are correct. Answer: E Difficulty: 2 Medium Topic: An Overview of Forecasting Techniques Learning Objective: Describe some important types of forecasting applications. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 34) Which of the following are costs of an inaccurate forecast? A) Lost sales B) Inventory C) An understaffed office D) Lower profits E) All of the answers choices are correct. Answer: D Difficulty: 2 Medium Topic: An Overview of Forecasting Techniques Learning Objective: Identify two common measures of the accuracy of forecasting methods. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) Time-series data may exhibit which of the following behaviors? A) Trend B) Seasonality C) Cycles D) Irregularities E) All of the answers choices are correct Answer: E Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

36) Gradual, long-term movement in time-series values is called: A) seasonal variation. B) trend. C) cycles. D) irregular variation. E) random variation. Answer: B Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 37) The last-value forecasting method: A) is quick and easy to prepare. B) is easy for users to understand. C) ignores all values except one. D) All of the answers choices are correct. E) None of the answer choices is correct. Answer: D Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) Using the latest value in a sequence of data to forecast the next period is: A) a moving-average forecast. B) a last-value forecast. C) an exponentially smoothed forecast. D) a causal forecast. E) None of the answer choices is correct. Answer: B Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10 Copyright © 2019 McGraw-Hill

39) Refer to the following data: Period 1 2 3 4

Demand 58 59 60 61

What is the last-value forecast for the next period? A) 58 B) 62 C) 60 D) 61 E) None of the answer choices is correct. Answer: D Explanation: The last value method assumes that the next data point will be the same as the last. In this case, the last value was 61 so that becomes the forecast for the next period. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

40) Refer to the following data: Period 1 2 3 4

Demand 58 59 60 61

What is the moving-average forecast for the next period based on the last three periods? A) 58 B) 62 C) 60 D) 61 E) None of the answer choices is correct. Answer: C Explanation: Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 41) In order to increase the responsiveness of a forecast made using the moving-average method, the number of values in the average should be: A) decreased. B) increased. C) multiplied by a larger α. D) multiplied by a smaller α. E) None of the answer choices is correct. Answer: A Difficulty: 1 Easy Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

42) Which of the following smoothing constants would make an exponential smoothing forecast equivalent to a last-value forecast? A) 0 B) 0.01 C) 0.1 D) 0.5 E) 1 Answer: E Explanation: The exponential smoothing formula with α = 1 reduces to the last-value formula. Forecast = α(Last Value) + (1 − α)(Last Forecast) = 1(Last Value) + (1 − 1)(Last Forecast) = Last Value. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 43) Given an actual latest demand of 59, a previous forecast of 64, and α = 0.3, what would be the forecast for the next period using the exponential smoothing method? A) 36.9 B) 57.5 C) 60.5 D) 62.5 E) 65.5 Answer: D Explanation: Forecast = α(Last Value) + (1 − α)(Last Forecast) = 0.3(59) + (1 − 0.3)64 = 62.5. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

44) Given an actual latest demand of 105, a previous forecast of 97, and α = 0.4, what would be the forecast for the next period using the exponential smoothing method? A) 80.8 B) 93.8 C) 100.2 D) 101.8 E) 108.2 Answer: C Explanation: Forecast = α(Last Value) + (1 - α)(Last Forecast) = 0.4(105) + (1 - 0.4)97 = 100.2. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 45) Which of the following possible values of α would cause exponential smoothing to respond the most quickly to forecast errors? A) 0 B) 0.01 C) 0.05 D) 0.1 E) 0.15 Answer: E Difficulty: 1 Easy Topic: The Time-Series Forecasting Methods in Perspective Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Analytical Thinking Accessibility: Keyboard Navigation

46) In exponential smoothing with trend, the forecast consists of: A) an exponentially smoothed forecast and a smoothed trend factor. B) the old forecast adjusted by a trend factor. C) the old forecast and a smoothed trend factor. D) a moving-average and a trend factor. E) None of the answer choices is correct. Answer: A Difficulty: 1 Easy Topic: The Time-Series Forecasting Methods in Perspective Learning Objective: Describe several forecasting methods that use the pattern of historical data to forecast a future value. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 47) The mean absolute deviation is used to: A) estimate the trend line. B) eliminate forecast errors. C) measure forecast accuracy. D) seasonally adjust the forecast. E) All of the answers choices are correct. Answer: C Difficulty: 2 Medium Topic: A Case Study: The Computer Club Warehouse (CCW) Problem Learning Objective: Identify two common measures of the accuracy of forecasting methods. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

48) Given forecast errors of 4, 8, and −3, what is the mean absolute deviation? A) 3 B) 4 C) 5 D) 6 E) 9 Answer: C Explanation: Mean absolute deviation is the average of the absolute values of the forecasting errors.

Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 49) Given forecast errors of 4, 8, and −3, what is the mean square error? A) 5 B) 9 C) 25 D) 29.67 E) 89 Answer: D Explanation: Mean squared error is the average of the squares of the forecasting errors.

50) Given forecast errors of 5, 0, −4, and 3, what is the mean absolute deviation? A) 1 B) 2 C) 2.5 D) 3 E) 12 Answer: D Explanation: Mean absolute deviation is the average of the absolute values of the forecasting errors.

Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 51) Given forecast errors of 5, 0, −4, and 3, what is the mean square error? A) 3 B) 4 C) 12 D) 12.5 E) 50 Answer: D Explanation: Mean squared error is the average of the squares of the forecasting errors.

52) Given the following historical data, what is the moving-average forecast for period 6 based on the last three periods? Period 1 2 3 4 5

Value 73 68 65 72 67

A) 67 B) 68 C) 69 D) 100 E) 115 Answer: B Explanation: Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

53) Given the following historical data, what is the moving-average forecast for period 6 based on the last three periods? Period 1 2 3 4 5

Value 19 20 18 19 17

A) 17 B) 18 C) 19 D) 20 E) 18.5 Answer: B Explanation: Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 54) Given forecast errors of −5, -10, and 15, what is the mean absolute deviation? A) 0 B) 5 C) 10 D) 30 E) None of the answer choices is correct. Answer: C Explanation: Mean absolute deviation is the average of the absolute values of the forecasting errors. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

55) The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year 5 years ago 4 years ago 3 years ago 2 years ago Last year

Enrollments 15,000 16,000 18,000 20,000 21,000

What is the forecast for this year using the last-value forecasting method? A) 18,750 B) 19,500 C) 21,000 D) 22,650 E) 22,800 Answer: C Explanation: The last-value forecast assumes that the next period will be the same as the previous. In this case, the forecast for this year is the same as last year, 21,000. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Enrollments 15,000 16,000 18,000 20,000 21,000

What is the forecast for this year using a moving-average forecast based on the last four years? A) 18,750 B) 19,500 C) 21,000 D) 22,650 E) 22,800 Answer: A Explanation: Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

57) The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year 5 years ago 4 years ago 3 years ago 2 years ago Last year

Enrollments 15,000 16,000 18,000 20,000 21,000

What is the forecast for this year using exponential smoothing with α = 0.5, if the forecast for two years ago was 16,000? A) 18,750 B) 19,500 C) 21,000 D) 22,650 E) 22,800 Answer: B Explanation: Alpha (α) = 0.5 Year Enrollments Forecast 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 16,000 Last year This year

21,000

18,000 19,500

New Forecast

0.5(20,000)+(1-0.5)(16,000) = 18,000 0.5(21,000)+(1-0.5)(18,000) = 19,500

Difficulty: 3 Hard Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Enrollments 15,000 16,000 18,000 20,000 21,000

What is the forecast for this year using exponential smoothing with trend if α = 0.5 and β = 0.3? Assume the forecast for last year was 21,000 and the forecast for two years ago was 19,000, and that the trend estimate for last year's forecast was 1,500. A) 18,750 B) 19,500 C) 21,000 D) 22,500 E) 22,800 Answer: D Explanation: Latest trend = α(Last value − Next-to-last value) + (1 − α)(Last forecast − Next-to-last forecast) = 0.5(21,000 − 20,000) + (1 − 0.5)(21,000 − 19,000) = 1,500 Estimated trend = β(Latest trend) + (1 − β)(Last estimate of trend) = 0.3(1,500) + 0.7(1,500) = 1,500 Forecast = α(Last value) + (1 − α)(Last forecast) + Estimated trend = 0.5(21,000) + (1 − 0.5)(21,000) + 1,500 = 22,500 Difficulty: 3 Hard Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

59) The business analyst for Ace Business Machines, Inc. wants to forecast this year's demand for manual typewriters based on the following historical data: Time Period 5 years ago 4 years ago 3 years ago 2 years ago Last year

Demand 900 700 600 500 300

What is the forecast for this year using the last-value forecasting method? A) 163 B) 180 C) 300 D) 467 E) 510 Answer: C Explanation: The last-value forecast assumes that the next period will be the same as the previous. In this case, the forecast for this year is the same as last year, 300. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Demand 900 700 600 500 300

What is the forecast for this year using a moving-average forecast based on the last three years? A) 163 B) 180 C) 300 D) 467 E) 510 Answer: D Explanation: Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

61) The business analyst for Ace Business Machines, Inc. wants to forecast this year's demand for manual typewriters based on the following historical data: Time Period 5 years ago 4 years ago 3 years ago 2 years ago Last year

Demand 900 700 600 500 300

What is the forecast for this year using exponential smoothing with α = 0.4, if the forecast for two years ago was 750? A) 163 B) 180 C) 300 D) 467 E) 510 Answer: E Explanation: Alpha (α) = 0.4 Year 5 years ago 4 years ago 3 years ago 2 years ago Last year This year

Demand 900 700 600 500 300

Forecast

New Forecast

700 650 510

0.4(500) + (1−0.4)(750) = 650 0.4(300) + (1−0.4)(650) = 510

# of students 83 110 95 80 65 50

What is the forecast for this year using the last-value forecasting method? A) 49 B) 50 C) 52 D) 65 E) 78 Answer: B Explanation: The last-value forecast assumes that the next period will be the same as the previous. In this case, the forecast for this week is the same as last week, 50. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

63) Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data: Week 6 weeks ago 5 weeks ago 4 weeks ago 3 weeks ago 2 weeks ago Last week

# of students 83 110 95 80 65 50

What is the forecast for this year using a moving-average forecast based on the last three weeks? A) 49 B) 50 C) 52 D) 65 E) 78 Answer: D Explanation: Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

# of students 83 110 95 80 65 50

What is the forecast for this year using exponential smoothing with α = 0.2, if the forecast for two weeks ago was 90? A) 49 B) 50 C) 52 D) 65 E) 78 Answer: E Explanation: Alpha (α) = 0.2 Period 6 weeks ago 5 weeks ago 4 weeks ago 3 weeks ago 2 weeks ago Last week This week

Students Forecast 83 110 95 80 65 90 50 85 78

New Forecast

0.2(65) + (1-0.2)(90) = 85 0.2(50) + (1-0.2)(85) = 78

65) Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data: Week 6 weeks ago 5 weeks ago 4 weeks ago 3 weeks ago 2 weeks ago Last week

# of students 83 110 95 80 65 50

What is the forecast for this week using exponential smoothing with trend if α = 0.5 and β = 0.1? Assume the forecast for last week was 65 and the forecast for two weeks ago was 75, and that the trend estimate for last week's forecast was −5. A) 49 B) 50 C) 52 D) 65 E) 78 Answer: C Explanation: Latest trend = α(Last value − Next-to-last value) + (1 − α)(Last forecast − Next-to-last forecast) = 0.5(50 − 65) + (1 − 0.5)(65 − 75) = −12.5 Estimated trend = β(Latest trend) + (1 − β)(Last estimate of trend) = 0.1(−12.5) + 0.9(−5) = −5.75 Forecast = α(Last value) + (1 − α)(Last forecast) + Estimated trend = 0.5(50) + (1 − 0.5)(65) + (−5.75) = 51.75 ≅ 52 Difficulty: 3 Hard Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

66) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

What is the forecast for this year using the last-value forecasting method? A) 22,000 B) 20,000 C) 18,000 D) 15,000 E) 12,000 Answer: B Explanation: The last-value forecast assumes that the next period will be the same as the previous. In this case, the forecast for this year is the same as last year, 20,000. Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

67) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

What is the forecast for this year using a moving-average forecast based on the last four years? A) 22,000 B) 20,000 C) 18,000 D) 15,000 E) 12,000 Answer: D Explanation: Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Apply these methods either by hand or with the software provided. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

68) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

What is the forecast for this year using exponential smoothing with α = 0.2, if the forecast for last year was 15,000? A) 20,000 B) 19,000 C) 17,500 D) 16,000 E) 15,000 Answer: D Explanation: Alpha (α) = 0.2 period 4 years ago 3 years ago 2 years ago

# Sold 10,000 12,000 18,000

Forecast

New Forecast

Last year

20,000

15,000

0.2(20,000)+(1−0.2)(15,000) = 16,000

This year

16,000

69) An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

The previous trend line has predicted 18,500 for two years ago, and 19,700 for last year. What was the mean absolute deviation for these forecasts? A) 100 B) 200 C) 400 D) 500 E) 800 Answer: C Explanation: Year 4 years ago 3 years ago 2 years ago Last year

# Sold 10,000 12,000 18,000 20,000

Forecast

Absolute Value of Error

18,500 19,700

500 300

70) A manager uses the equation y = 40,000 + 150x to predict monthly receipts. What is the forecast for July if x = 0 in April? A) 40,450 B) 40,600 C) 42,100 D) 42,250 E) 42,400 Answer: A Explanation: If x = 0 in April, x = 3 in July and the equation for July receipts becomes y = 40,000 + 150x = 40,000 + 150(3) = 40,450 Difficulty: 2 Medium Topic: Causal Forecasting With Linear Regression Learning Objective: Describe and apply an approach to forecasting that relates the quantity of interest to one or more other quantities. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 71) The equation y = 350 − 2.5x is used to predict quarterly demand where x = 0 in the second quarter of last year. Quarterly seasonal factors are Q1 = 1.5, Q2 = 0.8, Q3 = 1.1, and Q4 = 0.6. What is the forecast for the last quarter of this year? A) 199.5 B) 201 C) 266 D) 268 E) 335 Answer: B Explanation: For the last quarter of this year, x = 6. Therefore, unadjusted sales for Q4 of this year are given by y = 350 − 2.5x = 350 − 2.5(6) = 335. The seasonal factor for Q4 is 0.6, so seasonally adjusted receipts are given by Seasonally adjusted receipts = unadjusted sales × seasonal factor = 335 × 0.6 = 201. Difficulty: 3 Hard Topic: Causal Forecasting With Linear Regression Learning Objective: Describe and apply an approach to forecasting that relates the quantity of interest to one or more other quantities. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

72) The primary method for causal forecasting is: A) sensitivity analysis. B) linear regression. C) moving-average. D) exponential smoothing. E) the Delphi method. Answer: B Difficulty: 1 Easy Topic: Causal Forecasting With Linear Regression Learning Objective: Describe and apply an approach to forecasting that relates the quantity of interest to one or more other quantities. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 73) Which of the following is not a type of judgmental forecasting? A) Managerial opinion B) Sales force composite C) Time-series analysis D) The Delphi method E) Consumer market survey Answer: C Difficulty: 2 Medium Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 74) Which of the following would be considered a possible drawback of using executive opinions to develop a forecast? A) It is difficult to interpret the results. B) Responsibility is diffused for the forecast. C) Extensive use of computers is needed. D) It brings together the knowledge of top managers. E) Forecasters are sometimes overly influenced by recent events. Answer: B Difficulty: 2 Medium Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 36 Copyright © 2019 McGraw-Hill

75) Which of the following would be an advantage of using a sales force composite to develop a demand forecast? A) The sales staff is least affected by changing customer needs. B) The sales force can easily distinguish between customer desires and probable actions. C) The sales staff is often aware of customer's future plans. D) Salespeople are least likely to be biased by sales quotas. E) None of the answer choices is correct. Answer: C Difficulty: 2 Medium Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 76) The forecasting method which uses anonymous questionnaires to achieve a consensus forecast is: A) sales force composites. B) consumer surveys. C) the Delphi method. D) time-series analysis. E) executive opinions. Answer: C Difficulty: 1 Easy Topic: Judgmental Forecasting Methods Learning Objective: Describe several forecasting methods that use expert judgment. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

Sales 10,000 11,000 7,500 8,000 15,000 17,000 10,500 11,500

A) 0.74 B) 0.99 C) 1.14 D) 1.24 E) 1.29 Answer: D Explanation: Seasonal Factor =

= =

≅ 1.24

Difficulty: 2 Medium Topic: Applying Time-Series Forecasting Methods to the Case Study Learning Objective: Adjust forecasting data to consider seasonal patterns. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 11 Queueing Models 1) The goal of queuing analysis is to minimize customer waiting lines. 2) Queueing models enable finding an appropriate balance between the cost of service and the amount of waiting. 3) The cost of customer waiting is easy to estimate. 4) Most queueing models assume that the form of the probability distribution of interarrival times is an exponential distribution. 5) The only distribution of interarrival times that fits having random arrivals is the exponential distribution. 6) The lack-of-memory property refers to a customer's willingness to wait in line even though there are other customers that will be served first. 7) The number of customers in a system is the number in the queue plus one. 8) Queueing models conventionally assume that the queue can hold an unlimited number of customers. 9) Queue discipline refers to the willingness of customers to wait in line for service. 10) A loading dock with two servers who work together as a team would be an example of a multiple-server system. 11) The most commonly used queueing models assume a service rate that is exponential. 12) The exponential distribution will always provide a reasonably close approximation of the true service-time distribution. 13) The standard deviation for the degenerative distribution equals zero. 14) Managers who oversee queueing systems are usually concerned with how many customers are waiting and how long they will have to wait. 15) A queueing system is said to be in a "steady state" when customers arrive at a constant rate, that is, without any variability. 16) The expected waiting time in line is equal to the expected number of customers in line divided by the arrival rate. 17) The utilization factor is the ratio of the arrival rate to the service rate. 18) All single-server queueing models require the utilization factor to be less than 1. 1 Copyright © 2019 McGraw-Hill

19) In a single-server system, the utilization factor is equal to the mean arrival rate divided by the mean service rate. 20) Waiting lines occur even in systems that are less that 100% utilized because of variability in service rates and/or arrival rates. 21) A system has one service facility that can service 10 customers per hour. The customers arrive at an average rate of 6 per hour. In this case, no waiting line will form. 22) For a system that has a high utilization factor, decreasing the service rate will have only a negligible effect on customer waiting time. 23) The assumption of constant service times cannot be used with human servers because of the inevitable variability. 24) In a nonpreemptive priority system, customers are served in the order in which they arrive in the queue. 25) In a preemptive priority system, the lowest-priority customer being served is ejected back into the queue whenever a higher-priority customer enters the queueing system. 26) The reason for using priorities is to decrease the waiting times for high-priority customers. 27) When designing a single-server queueing system, giving a relatively high utilization factor to the server ensures that the system is working efficiently. 28) Decreasing the variability of service times, without any change in the mean, improves the performance of a single-server queueing system substantially. 29) Multiple-server queueing systems can perform satisfactorily with somewhat higher utilization factors than can single-server queueing systems. 30) Applying nonpreemptive priorities improves the measures of performance in the top priority class even more than applying preemptive priorities. 31) Choosing the number of servers in a system involves finding an appropriate trade-off between the cost of the servers and the amount of waiting. 32) The goal of queueing analysis is to minimize: A) the sum of customer waiting costs and service costs. B) the sum of customer waiting time and service time. C) service costs. D) customer waiting time. E) None of the answer choices is correct.

33) A single server queueing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes. The arrival rate is: A) 6 per hour. B) 7.5 per hour. C) 8 per hour. D) 10 per hour. E) 12.5 per hour. 34) The term queue discipline refers to: A) the willingness of customers to wait in line for service. B) having multiple waiting lines without customers switching from line to line. C) the order in which customers are processed. D) the reason waiting occurs in underutilized systems. E) None of the answer choices is correct. 35) A queueing system has four crews with three members each. The number of "servers" is: A) 3. B) 4. C) 7. D) 12. E) 1. 36) Which of the following is not an example of a commercial service system? A) ATM cash machine B) Brokerage service C) Travel agency D) Tool crib E) Call center 37) If a manager increases the system utilization standard (assuming no change in the customer arrival rate) what happens to the customer waiting time? A) It increases exponentially. B) It increases proportionally. C) It decreases proportionally. D) It decreases exponentially. E) No change. 38) Which of the following is not generally considered as a measure of performance in queueing analysis? A) The average number waiting in line B) The average number in the system C) The system utilization factor D) The cost of servers plus customer waiting cost E) Service time

39) Which of the following will equal the average time that a customer is in the system? The average number in the system divided by the arrival rate. The average number in the system multiplied by the arrival rate. The average time in line plus the average service time. A) I only. B) II only. C) III only. D) II and III only. E) I and III only. 40) As the ratio of arrival rate to service rate is increased, which of the following is likely? A) Customers move through the system in less time because utilization is increased. B) Customers move through the system more slowly because utilization is increased. C) Utilization is decreased because of the added strain on the system. D) The average number in the system decreases. E) None of the answer choices is correct. 41) Which of these would increase system utilization? A) An increase in the service rate B) An increase in the arrival rate C) An increase in the number of servers D) A decrease in service time E) All of the answers choices are correct 42) A single bay car wash with an exponential arrival rate and service time has cars arriving an average of 10 minutes apart, and an average service time of 4 minutes. The utilization factor is: A) 0.24. B) 0.4. C) 0.67. D) 2.5 E) None of the answer choices is correct. 43) There are 5 servers in a system with an arrival rate of 6 per hour and a service time of 20 minutes. What is the system utilization? A) 0.1 B) 0.3 C) 0.4 D) 1.2 E) 2.0

44) A multiple-server queueing system with an exponential arrival rate and service time has a mean arrival rate of 4 customers per hour and a mean service time of 18 minutes per customer. The minimum number of servers required to keep the utilization factor under 1 is: A) 1. B) 2. C) 3. D) 4. E) 5. 45) A single-server queueing system has an average service time of 16 minutes per customer, which is exponentially distributed. The manager is thinking of converting to a system with a constant service time of 16 minutes. The arrival rate will remain the same. The effect will be to: A) increase the utilization factor. B) decrease the utilization factor. C) increase the average waiting time. D) decrease the average waiting time. E) not have any effect since the service time is unchanged. 46) A multiple-server system has customers arriving at an average rate of five per hour and an average service time of forty minutes. The minimum number of servers for this system to have a utilization factor under 1 is: A) 2. B) 3. C) 4. D) 5. E) None of the answer choices is correct. 47) Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. What is the system utilization? A) 0.6 B) 0.7 C) 0.8 D) 0.9 E) 1

48) Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. What is the average number of customers waiting in line? A) 1.633 B) 2.333 C) 2.5 D) 3.966 E) 4 49) Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. How many minutes does the average customer wait in line? A) 7 B) 8 C) 9 D) 10 E) 11 50) Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. How many minutes does the average customer spend in the system? A) 7. B) 8. C) 9. D) 10. E) 11. 51) During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential). What is the average number of customers waiting for service if 6 clerks are used? A) 0 B) 0.01 C) 0.1 D) 1 E) 10

52) During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential). What is the minimum number of clerks needed to keep the average time in the system under 5 minutes? A) 2 B) 3 C) 4 D) 5 E) 6 53) During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential). If clerk cost is $30 per hour and customer waiting time represents a cost of $20 per hour, how many clerks can be justified on a cost basis? A) 2. B) 3. C) 4. D) 5. E) 6. 54) Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times). What is the average number of customers in the system with 8 servers? A) 2 B) 3 C) 4 D) 5 E) 6 55) Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times). What is the minimum number of servers needed to keep the average time in the system under 6 minutes? A) 2 B) 3 C) 4 D) 5 E) 6

56) Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times). What is the system utilization factor if 5 servers are used? A) 0.6. B) 0.7. C) 0.8. D) 0.9. E) 1. 57) Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times). If there are 4 servers, what is the average time it takes in minutes to rent a videotape? A) 2 B) 3 C) 4 D) 5 E) 6 58) Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times). If there are 4 servers, what is the probability of three or fewer customers in the system? A) 0.19 B) 0.23 C) 0.63 D) 0.68 E) 0.79 59) Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times). What is the minimum number of servers needed to achieve an average time in the system of less than three minutes? A) 2 B) 3 C) 4 D) 5 E) 6 60) A multiple priority queueing model assumes that: A) arrival rates are exponentially distributed. B) service rate is exponentially distributed. C) items are serviced in the order of arrival. D) items are serviced in order of priority class. E) service activities are preemptive. 8 Copyright © 2019 McGraw-Hill

61) Which of the following is not an assumption of a multiple priority queueing model? A) Exponential interarrival times. B) Exponential service times. C) Customers are processed in the order of arrival. D) Customers wait in a single line. E) All of the answers choices are assumptions of a multiple priority queueing model. 62) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the overall arrival rate per hour? A) 3 B) 4 C) 5 D) 8 E) 15 63) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the system utilization factor? A) 0.45 B) 0.50 C) 0.55 D) 0.65 E) 0.80

64) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in line (in minutes) for a high priority item? A) 2 B) 5 C) 24 D) 35 E) 54 65) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in line (in minutes) for a low priority item? A) 2 B) 5 C) 24 D) 35 E) 54

66) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in the system (in minutes) for a high priority item? A) 2 B) 5 C) 24 D) 35 E) 54 67) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in the system (in minutes) for a low priority item? A) 2 B) 5 C) 24 D) 35 E) 54 68) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

69) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average number of low priority items waiting in line for service? A) 0 B) 0.24 C) 1.74 D) 1.98 E) 2.22 70) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average number of all items waiting in line for service? A) 0 B) 0.24 C) 1.74 D) 1.98 E) 2.22 71) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. What is the approximate average time in minutes that truckers wait to be seated? A) 2.7 B) 4.5 C) 8.4 D) 13.6 E) 15.8

72) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. What is the approximate average time in minutes that non-truckers wait to be seated? A) 2.7 B) 4.5 C) 8.4 D) 13.6 E) 15.8 73) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. On average, how many parties of truckers are waiting to be seated? A) 0.27. B) 0.52. C) 0.88. D) 1.36. E) 1.75. 74) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. On average, how many parties of non-truckers are waiting to be seated? A) 0.27. B) 0.52. C) 0.88. D) 1.36. E) 1.75. 75) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. On average, how much longer in minutes do parties of non-truckers spend in the system, compared to parties of truckers? A) 4. B) 7. C) 11. D) 15. E) It is impossible to determine without more information. 13 Copyright © 2019 McGraw-Hill

76) For a single-server queueing system, which of the following is TRUE? I. A high utilization factor will result in a system that performs well. II. A high utilization factor will result in a system that performs poorly. III. A low utilization factor will result in a system that performs efficiently. A) I only. B) II only. C) III only. D) I and II only. E) I and III only. 77) For a single-server queueing system, which of the following is FALSE? I. Decreasing the variability of service times improves the performance of the system. II. Decreasing the variability of service times reduces the performance of the system. III. Increasing the variability of arrival times improves the performance of the system. A) I only B) II only C) III only D) I and II only E) I and III only 78) A firm has two separate phone systems for customers to use when contacting the firm. A manager is considering combining the two systems into a single system (with the same number of total servers as the two existing systems). What is likely to be the result of this change? I. The new system will have higher utilization of servers. II. The new system will have longer wait times for customers. III. The new system will have shorter wait times for customers. A) I only. B) II only. C) III only. D) I and II only. E) II and III only.

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 11 Queueing Models 1) The goal of queuing analysis is to minimize customer waiting lines. Answer: FALSE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) Queueing models enable finding an appropriate balance between the cost of service and the amount of waiting. Answer: TRUE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) The cost of customer waiting is easy to estimate. Answer: FALSE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) Most queueing models assume that the form of the probability distribution of interarrival times is an exponential distribution. Answer: TRUE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 1 Copyright © 2019 McGraw-Hill

5) The only distribution of interarrival times that fits having random arrivals is the exponential distribution. Answer: TRUE Difficulty: 2 Medium Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) The lack-of-memory property refers to a customer's willingness to wait in line even though there are other customers that will be served first. Answer: FALSE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Identify the characteristics of the probability distributions that are commonly used in queueing models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) The number of customers in a system is the number in the queue plus one. Answer: FALSE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) Queueing models conventionally assume that the queue can hold an unlimited number of customers. Answer: TRUE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

9) Queue discipline refers to the willingness of customers to wait in line for service. Answer: FALSE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) A loading dock with two servers who work together as a team would be an example of a multiple-server system. Answer: FALSE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) The most commonly used queueing models assume a service rate that is exponential. Answer: TRUE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) The exponential distribution will always provide a reasonably close approximation of the true service-time distribution. Answer: FALSE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) The standard deviation for the degenerative distribution equals zero. Answer: TRUE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) Managers who oversee queueing systems are usually concerned with how many customers are waiting and how long they will have to wait. Answer: TRUE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) A queueing system is said to be in a "steady state" when customers arrive at a constant rate, that is, without any variability. Answer: FALSE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) The expected waiting time in line is equal to the expected number of customers in line divided by the arrival rate. Answer: TRUE Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

17) The utilization factor is the ratio of the arrival rate to the service rate. Answer: TRUE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) All single-server queueing models require the utilization factor to be less than 1. Answer: TRUE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) In a single-server system, the utilization factor is equal to the mean arrival rate divided by the mean service rate. Answer: TRUE Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) Waiting lines occur even in systems that are less that 100% utilized because of variability in service rates and/or arrival rates. Answer: TRUE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

21) A system has one service facility that can service 10 customers per hour. The customers arrive at an average rate of 6 per hour. In this case, no waiting line will form. Answer: FALSE Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Apply AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) For a system that has a high utilization factor, decreasing the service rate will have only a negligible effect on customer waiting time. Answer: FALSE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) The assumption of constant service times cannot be used with human servers because of the inevitable variability. Answer: FALSE Difficulty: 1 Easy Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 24) In a nonpreemptive priority system, customers are served in the order in which they arrive in the queue. Answer: FALSE Difficulty: 1 Easy Topic: Some Single-Server Queueing Models Learning Objective: Describe the main types of basic queueing models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

25) In a preemptive priority system, the lowest-priority customer being served is ejected back into the queue whenever a higher-priority customer enters the queueing system. Answer: TRUE Difficulty: 1 Easy Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) The reason for using priorities is to decrease the waiting times for high-priority customers. Answer: TRUE Difficulty: 1 Easy Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) When designing a single-server queueing system, giving a relatively high utilization factor to the server ensures that the system is working efficiently. Answer: FALSE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) Decreasing the variability of service times, without any change in the mean, improves the performance of a single-server queueing system substantially. Answer: TRUE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

29) Multiple-server queueing systems can perform satisfactorily with somewhat higher utilization factors than can single-server queueing systems. Answer: TRUE Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) Applying nonpreemptive priorities improves the measures of performance in the top priority class even more than applying preemptive priorities. Answer: FALSE Difficulty: 2 Medium Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) Choosing the number of servers in a system involves finding an appropriate trade-off between the cost of the servers and the amount of waiting. Answer: TRUE Difficulty: 1 Easy Topic: Economic Analysis of the Number of Servers to Provide Learning Objective: Apply economic analysis to determine how many servers should be provided in a queueing system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

32) The goal of queueing analysis is to minimize: A) the sum of customer waiting costs and service costs. B) the sum of customer waiting time and service time. C) service costs. D) customer waiting time. E) None of the answer choices is correct. Answer: A Difficulty: 1 Easy Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 33) A single server queueing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes. The arrival rate is: A) 6 per hour. B) 7.5 per hour. C) 8 per hour. D) 10 per hour. E) 12.5 per hour. Answer: A Explanation: for λ (the arrival rate) we see that

rearranging to solve

Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

34) The term queue discipline refers to: A) the willingness of customers to wait in line for service. B) having multiple waiting lines without customers switching from line to line. C) the order in which customers are processed. D) the reason waiting occurs in underutilized systems. E) None of the answer choices is correct. Answer: C Difficulty: 2 Medium Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) A queueing system has four crews with three members each. The number of "servers" is: A) 3. B) 4. C) 7. D) 12. E) 1. Answer: B Explanation: Each crew is considered a server because they work together. Difficulty: 2 Medium Topic: Elements of a Queueing Model Learning Objective: Describe the elements of a queueing model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 36) Which of the following is not an example of a commercial service system? A) ATM cash machine B) Brokerage service C) Travel agency D) Tool crib E) Call center Answer: D Difficulty: 2 Medium Topic: Some Examples of Queueing Systems Learning Objective: Give many examples of various types of queueing systems that are commonly encountered. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 10 Copyright © 2019 McGraw-Hill

37) If a manager increases the system utilization standard (assuming no change in the customer arrival rate) what happens to the customer waiting time? A) It increases exponentially. B) It increases proportionally. C) It decreases proportionally. D) It decreases exponentially. E) No change. Answer: A Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) Which of the following is not generally considered as a measure of performance in queueing analysis? A) The average number waiting in line B) The average number in the system C) The system utilization factor D) The cost of servers plus customer waiting cost E) Service time Answer: E Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

39) Which of the following will equal the average time that a customer is in the system? I. The average number in the system divided by the arrival rate. II. The average number in the system multiplied by the arrival rate. III. The average time in line plus the average service time. A) I only. B) II only. C) III only. D) II and III only. E) I and III only. Answer: E Explanation: W (the expected waiting time in the system) is given by the equation (where Wq is the time in line and is the average service time). W can also be found via Little's Law. L = λW. Rearranging to solve for W shows that (where L is the average number in the system and λ is the arrival rate. Difficulty: 3 Hard Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 40) As the ratio of arrival rate to service rate is increased, which of the following is likely? A) Customers move through the system in less time because utilization is increased. B) Customers move through the system more slowly because utilization is increased. C) Utilization is decreased because of the added strain on the system. D) The average number in the system decreases. E) None of the answer choices is correct. Answer: B Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

41) Which of these would increase system utilization? A) An increase in the service rate B) An increase in the arrival rate C) An increase in the number of servers D) A decrease in service time E) All of the answers choices are correct Answer: B Difficulty: 2 Medium Topic: Measures of Performance for Queueing Systems Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 42) A single bay car wash with an exponential arrival rate and service time has cars arriving an average of 10 minutes apart, and an average service time of 4 minutes. The utilization factor is: A) 0.24. B) 0.4. C) 0.67. D) 2.5 E) None of the answer choices is correct. Answer: B Explanation: The utilization factor can be calculated to be 0.4. First, convert inter-arrival time to arrival rate (

) and convert service

time to service rate (

Difficulty: 3 Hard Topic: Some Single-Server Queueing Models Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

43) There are 5 servers in a system with an arrival rate of 6 per hour and a service time of 20 minutes. What is the system utilization? A) 0.1 B) 0.3 C) 0.4 D) 1.2 E) 2.0 Answer: C Explanation: The utilization factor can be calculated to be 0.4. First, convert service time to service rate

Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 44) A multiple-server queueing system with an exponential arrival rate and service time has a mean arrival rate of 4 customers per hour and a mean service time of 18 minutes per customer. The minimum number of servers required to keep the utilization factor under 1 is: A) 1. B) 2. C) 3. D) 4. E) 5. Answer: B Explanation: First, convert service time to service rate Next, set the utilization equal to 1 and solve for s.

Round up to 2 servers. Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 14 Copyright © 2019 McGraw-Hill

45) A single-server queueing system has an average service time of 16 minutes per customer, which is exponentially distributed. The manager is thinking of converting to a system with a constant service time of 16 minutes. The arrival rate will remain the same. The effect will be to: A) increase the utilization factor. B) decrease the utilization factor. C) increase the average waiting time. D) decrease the average waiting time. E) not have any effect since the service time is unchanged. Answer: D Explanation: Constant service times will have less variation, which leads to a decrease in queue length and waiting time. Difficulty: 2 Medium Topic: Some Single-Server Queueing Models Learning Objective: Describe the main types of basic queueing models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 46) A multiple-server system has customers arriving at an average rate of five per hour and an average service time of forty minutes. The minimum number of servers for this system to have a utilization factor under 1 is: A) 2. B) 3. C) 4. D) 5. E) None of the answer choices is correct. Answer: C Explanation: First, convert service time to service rate (μ =

= 0.025 customers per minute = 1.5 customers per hour).

Next, set the utilization equal to 1 and solve for s. ρ=

=1⇔s=

= 3.33 servers.

Round up to 4 servers. Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Identify the key measures of performance for queueing systems and the relationships between these measures. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

47) Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. What is the system utilization? A) 0.6 B) 0.7 C) 0.8 D) 0.9 E) 1 Answer: B Explanation: First, convert service time to service rate

Difficulty: 3 Hard Topic: Some Single-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

49) Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. How many minutes does the average customer wait in line? A) 7 B) 8 C) 9 D) 10 E) 11 Answer: A Explanation: First, convert service time to service rate

50) Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. How many minutes does the average customer spend in the system? A) 7. B) 8. C) 9. D) 10. E) 11. Answer: D Explanation: First, convert service time to service rate

51) During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential). What is the average number of customers waiting for service if 6 clerks are used? A) 0 B) 0.01 C) 0.1 D) 1 E) 10 Answer: C Explanation: First, convert service time to service rate Using the MMs textbook spreadsheet, this results in Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

53) During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential). If clerk cost is $30 per hour and customer waiting time represents a cost of $20 per hour, how many clerks can be justified on a cost basis? A) 2. B) 3. C) 4. D) 5. E) 6. Answer: C Explanation: First, convert service time to service rate Using the MMs Economic Analysis textbook spreadsheet, we see that fewer than 4 servers will not be able to keep up with arrivals and 5 or more servers has a higher cost than 4 servers. Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 54) Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times). What is the average number of customers in the system with 8 servers? A) 2 B) 3 C) 4 D) 5 E) 6 Answer: C Explanation: First, convert inter-arrival time to arrival rate Using the MMs textbook spreadsheet, this results in Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 22 Copyright © 2019 McGraw-Hill

55) Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times). What is the minimum number of servers needed to keep the average time in the system under 6 minutes? A) 2 B) 3 C) 4 D) 5 E) 6 Answer: E Explanation: First, convert inter-arrival time to arrival rate Using the MMs textbook spreadsheet, trial and error show that with 6 servers average time in the system is 4.57 minutes but with 5 servers average time in the system increases to 6.22 minutes. Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 57) Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times). If there are 4 servers, what is the average time it takes in minutes to rent a videotape? A) 2 B) 3 C) 4 D) 5 E) 6 Answer: B Explanation: λ = 1 customer per minute, μ = 0.4 customer per minute Using the MMs textbook spreadsheet with 4 servers, average time in the system is 3.03 minutes. Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

58) Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times). If there are 4 servers, what is the probability of three or fewer customers in the system? A) 0.19 B) 0.23 C) 0.63 D) 0.68 E) 0.79 Answer: D Explanation: λ = 1 customer per minute, μ = 0.4 customer per minute Using the MMs textbook spreadsheet with 4 servers, the probability of three or fewer customers is the sum of the individual probabilities: P0 + P1 + P2 + P3 = 0.074 + 0.184 + 0.230 + 0.192 = 0.680 Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 59) Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times). What is the minimum number of servers needed to achieve an average time in the system of less than three minutes? A) 2 B) 3 C) 4 D) 5 E) 6 Answer: D Explanation: Using the MMs textbook spreadsheet, trial and error show that with 5 servers average time in the system is 2.63 minutes but with 4 servers average time in the system increases to 3.03 minutes. Difficulty: 3 Hard Topic: Some Multiple-Server Queueing Models Learning Objective: Apply a queueing model to determine the key measures of performance for a queueing system. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 25 Copyright © 2019 McGraw-Hill

60) A multiple priority queueing model assumes that: A) arrival rates are exponentially distributed. B) service rate is exponentially distributed. C) items are serviced in the order of arrival. D) items are serviced in order of priority class. E) service activities are preemptive. Answer: D Difficulty: 2 Medium Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 61) Which of the following is not an assumption of a multiple priority queueing model? A) Exponential interarrival times. B) Exponential service times. C) Customers are processed in the order of arrival. D) Customers wait in a single line. E) All of the answers choices are assumptions of a multiple priority queueing model. Answer: C Difficulty: 2 Medium Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

62) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the overall arrival rate per hour? A) 3 B) 4 C) 5 D) 8 E) 15 Answer: D Explanation: λTotal = λHigh + λLow = 5 + 3 = 8 customers per hour customers per hour customers per hour customers per hour Difficulty: 2 Medium Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

63) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the system utilization factor? A) 0.45 B) 0.50 C) 0.55 D) 0.65 E) 0.80 Answer: E

Explanation: Difficulty: 2 Medium Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

64) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in line (in minutes) for a high priority item? A) 2 B) 5 C) 24 D) 35 E) 54 Answer: B Explanation: Using the textbook spreadsheet Nonpreemptive Priorities, the average time in line (Wq) for high priority items is 0.079 hour (4.74 minutes). Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

65) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in line (in minutes) for a low priority item? A) 2 B) 5 C) 24 D) 35 E) 54 Answer: C Explanation: Using the textbook spreadsheet Nonpreemptive Priorities, the average time in line (Wq) for low priority items is 0.396 hour (23.75 minutes). Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

66) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in the system (in minutes) for a high priority item? A) 2 B) 5 C) 24 D) 35 E) 54 Answer: D Explanation: Using the textbook spreadsheet Nonpreemptive Priorities, the average time in system ( W ) for high priority items is 0.579 hour (34.74 minutes). Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

67) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average time in the system (in minutes) for a low priority item? A) 2 B) 5 C) 24 D) 35 E) 54 Answer: E Explanation: Using the textbook spreadsheet Nonpreemptive Priorities, the average time in system (W) for low priority items is 0.896 hour (53.76 minutes). Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

68) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average number of high priority items waiting in line for service? A) 0 B) 0.24 C) 1.74 D) 1.98 E) 2.22 Answer: B Explanation: Using the textbook spreadsheet Nonpreemptive Priorities, the average number of items in line (Lq) for high priority items is 0.237. Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

69) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average number of low priority items waiting in line for service? A) 0 B) 0.24 C) 1.74 D) 1.98 E) 2.22 Answer: D Explanation: Using the textbook spreadsheet Nonpreemptive Priorities, the average number of items in line (Lq) for low priority items is 1.98. Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

70) Priority High Low

Average Arrival Rate (exponential interarrival times) 3 per hour 5 per hour

Number of servers: Service rate:

5 2 per hour (exponential service times)

What is the average number of all items waiting in line for service? A) 0 B) 0.24 C) 1.74 D) 1.98 E) 2.22 Answer: E Explanation: Using the textbook spreadsheet Nonpreemptive Priorities, the average number of items in line (Lq) for high priority items is 0.237 and for low priority items is 1.98. The total number of items in line is 0.237 + 1.98 = 2.22. Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

71) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. What is the approximate average time in minutes that truckers wait to be seated? A) 2.7 B) 4.5 C) 8.4 D) 13.6 E) 15.8 Answer: A Explanation: First, convert service time to service rate λ = 6 parties per hour for both truckers and non-truckers and there are 10 servers (tables). Assuming non-trucker customers won't be asked to leave after being seated, this is a non-preemptive queueing system. Using the textbook spreadsheet Nonpreemptive Priorities, the average time waiting in line (Wq) for high priority items is 0.046 hour (2.76 minutes). Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

73) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. On average, how many parties of truckers are waiting to be seated? A) 0.27. B) 0.52. C) 0.88. D) 1.36. E) 1.75. Answer: A Explanation: First, convert service time to service rate λ = 6 parties per hour for both truckers and non-truckers and there are 10 servers (tables). Assuming non-trucker customers won't be asked to leave after being seated, this is a non-preemptive queueing system. Using the textbook spreadsheet Nonpreemptive Priorities, the average number waiting in line (Lq) for high priority items is 0.272 parties. Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

74) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. On average, how many parties of non-truckers are waiting to be seated? A) 0.27. B) 0.52. C) 0.88. D) 1.36. E) 1.75. Answer: D Explanation: First, convert service time to service rate λ = 6 parties per hour for both truckers and non-truckers and there are 10 servers (tables). Assuming non-trucker customers won't be asked to leave after being seated, this is a non-preemptive queueing system. Using the textbook spreadsheet Nonpreemptive Priorities, the average number waiting in line (Lq) for low priority items is 1.364 parties. Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

75) A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. On average, how much longer in minutes do parties of non-truckers spend in the system, compared to parties of truckers? A) 4. B) 7. C) 11. D) 15. E) It is impossible to determine without more information. Answer: C Explanation: First, convert service time to service rate λ = 6 parties per hour for both truckers and non-truckers and there are 10 servers (tables). Assuming non-trucker customers won't be asked to leave after being seated, this is a non-preemptive queueing system. Using the textbook spreadsheet Nonpreemptive Priorities, the average time in the system (W) for low priority items is 0.894 hour (53.64 minutes) and for high priority items is 0.712 hour (42.72 minutes). A difference of 10.92 minutes. Difficulty: 3 Hard Topic: Priority Queueing Models Learning Objective: Describe how differences in the importance of customers can be incorporated into priority queueing models. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

76) For a single-server queueing system, which of the following is TRUE? I. A high utilization factor will result in a system that performs well. II. A high utilization factor will result in a system that performs poorly. III. A low utilization factor will result in a system that performs efficiently. A) I only. B) II only. C) III only. D) I and II only. E) I and III only. Answer: B Difficulty: 2 Medium Topic: Some Insights About Designing Queueing Systems Learning Objective: Describe some key insights that queueing models provide about how queueing systems should be designed. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 77) For a single-server queueing system, which of the following is FALSE? I. Decreasing the variability of service times improves the performance of the system. II. Decreasing the variability of service times reduces the performance of the system. III. Increasing the variability of arrival times improves the performance of the system. A) I only B) II only C) III only D) I and II only E) I and III only Answer: A Difficulty: 2 Medium Topic: Some Insights About Designing Queueing Systems Learning Objective: Describe some key insights that queueing models provide about how queueing systems should be designed. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

78) A firm has two separate phone systems for customers to use when contacting the firm. A manager is considering combining the two systems into a single system (with the same number of total servers as the two existing systems). What is likely to be the result of this change? I. The new system will have higher utilization of servers. II. The new system will have longer wait times for customers. III. The new system will have shorter wait times for customers. A) I only. B) II only. C) III only. D) I and II only. E) II and III only. Answer: C Difficulty: 2 Medium Topic: Some Insights About Designing Queueing Systems Learning Objective: Describe some key insights that queueing models provide about how queueing systems should be designed. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 12 Computer Simulation: Basic Concepts 1) Managers can use simulation to obtain optimal answers for a wide range of problems. 2) Computers can simulate years of operation in seconds. 3) Simulation is basically an optimizing technique. 4) Simulation models are fairly easy to use and understand; therefore they can be used for a wide range of decisions. 5) A stochastic system is one that evolved over time according to a continuous probability distribution. 6) When dealing with relatively complex systems, computer simulation is an inexpensive option for decision makers. 7) Simulation is especially useful for situations too complex to be analyzed using analytical models. 8) Simulation enables a decision maker to experiment with a system and observe its behavior. 9) A simulation model is validated if it adequately depicts real system performance. 10) One purpose of running experiments on a simulation model is to answer "what-if" questions. 11) Simulation is often the first choice of decision makers instead of analytic models. 12) A number is a random number between 0 and 1 if it is generated in such a way that every possible number within this interval has an equal chance of occurring. 13) When using a random number table, it is important to always start at the same point of the table so that results may be replicated. 14) Random numbers can be generated in Excel by using the VLOOKUP function. 15) Computer simulation is a useful tool because it generates accurate information using very small samples. 16) Random observations can be generated in Excel by using the VLOOKUP function. 17) Computer simulation is only applicable to situations that have elements that can be described by random variables 18) Analytical methods are preferable to simulation if an appropriate analytic method is available.

19) A simulation model includes a description of the components of the system that is to be simulated. 20) A simulation clock keeps track of how long the simulation has run in real time. 21) The main procedure for advancing the time on the simulation clock is called next-event time advance. 22) Simulation will often give measures of performance as outputs. 23) It is always necessary to test the validity of a simulation model by comparing its results with those of an analytic study. 24) With the speed of computers, it is not necessary to limit the amount of factors considered in a simulation. 25) A simulation model is often formulated in terms of a flow diagram. 26) A flow diagram shows the output of a simulation run. 27) Animation can be used to display computer simulations in action. 28) A larger confidence interval is desirable for a measure of performance since it shows that the results are valid over a larger range. 29) One key advantage of computer simulation is that is makes full use of the simplifying approximations that are available. 30) A parameter analysis report is used to generate many replications of a computer simulation. 31) A Data Table can be used to "trick" Excel to perform many replications of a computer simulation.

32) Given this frequency distribution, the random number 0.2258 would be interpreted as a demand of: Demand 0 1 2 3

Frequency 38 22 22 18

A) 0. B) 1. C) 2. D) 3. E) 1 or 2. 33) Given this frequency distribution, the random number 0.5211 would be interpreted as a demand of: Demand 0 1 2 3

Frequency 38 22 22 18

A) 0. B) 1. C) 2. D) 3. E) 1 or 2. 34) Given this frequency distribution, the random number 0.9015 would be interpreted as a demand of: Demand 0 1 2 3

Frequency 38 22 22 18

35) The main reason that a large number of replications of a simulation would be made is: A) computers are usually used, and they can easily handle a large number of replications. B) it is part of the scientific approach. C) it is a form of sampling, and large samples give more accurate results than small samples. D) it is more likely to provide optimal answers. E) None of the answer choices is correct. 36) In order to generate more accurate results when using simulation: A) use a continuous distribution instead of a discreet distribution. B) increase the number of replications. C) increase the number of factors considered. D) All of the answers choices are correct. E) None of the answer choices is correct. 37) Which of the following would not be a probable reason for choosing simulation as a decision-making tool? A) The situation is too complex for a mathematical model. B) There is a limited time in which to obtain results. C) Good results have been obtained in the past using simulation. D) Users are able to understand the model. E) All of these are probable reasons for choosing simulation. 38) Which of the following is not a reason for simulation's popularity? A) It is simple to use and/or understand. B) Extensive software packages are available. C) Many situations are too complex for mathematical solutions. D) If can be used for a wide range of applications. E) It is typically an inexpensive approach. 39) If a simulation begins with the first random number, the first simulated value would be: Random numbers: 0.6246, 0.2594, 0.4055 Demand 0 1 2 3 4

Frequency 0.15 0.30 0.25 0.15 0.15

40) If a simulation begins with the first random number, the second simulated value would be: Random numbers: 0.6246, 0.2594, 0.4055 Demand 0 1 2 3 4

Frequency 0.15 0.30 0.25 0.15 0.15

A) 0. B) 1. C) 2. D) 3. E) 4. 41) If a simulation begins with the first random number, the third simulated value would be: Random numbers: 0.6246, 0.2594, 0.4055 Demand 0 1 2 3 4

Frequency 0.15 0.30 0.25 0.15 0.15

A) 0. B) 1. C) 2. D) 3. E) 4. 42) A manager is simulating the number of times a machine operator stops a machine to make adjustments. After careful study the manager found that the number of stops ranged from one to five per cycle and that each number of stops was equally likely. Using the random numbers 0.1835 and 0.3094 (in that order), the next two simulated cycles would respectively have stops for adjustment of: A) 2 and 2. B) 1 and 2. C) 2 and 1. D) 1 and 1. E) 2 and 3. 5 Copyright © 2019 McGraw-Hill

43) Which of the following would not be considered a main advantage of simulation? A) It permits experimentation with the system. B) It generates an optimal solution. C) It compresses time. D) It can serve as a training tool. E) All of the answers choices are advantages. 44) On cold mornings, the probability that David's car won't start is 0.22. When it doesn't start, he takes the bus and is late for work. When it does start, he drives to work on the freeway. Sixty-five percent of the time the freeway is clear, and he gets to work on time. The rest of the time he is late. Simulate 10 consecutive days' worth of trips to work using the random numbers given (use the smaller numbers to represent "car won't start" and "freeway clear"). Random numbers: Car 0.7772 0.2902 0.8120 0.2259 0.0527 0.2958 0.2891 0.0131 0.5219 0.9949

Traffic 0.2282 0.3674 0.1654 0.6909 0.7010 0.9802 0.5615 0.5604 0.4361 0.1405

How many times is David late for work because his car won't start? A) 0. B) 1. C) 2. D) 3. E) 4.

45) On cold mornings, the probability that David's car won't start is 0.22. When it doesn't start, he takes the bus and is late for work. When it does start, he drives to work on the freeway. Sixty-five percent of the time the freeway is clear, and he gets to work on time. The rest of the time he is late. Simulate 10 consecutive days' worth of trips to work using the random numbers given (use the smaller numbers to represent "car won't start" and "freeway clear"). Random numbers: Car 0.7772 0.2902 0.8120 0.2259 0.0527 0.2958 0.2891 0.0131 0.5219 0.9949

Traffic 0.2282 0.3674 0.1654 0.6909 0.7010 0.9802 0.5615 0.5604 0.4361 0.1405

How many times is David late for work? A) 1. B) 2. C) 3. D) 4. E) 5. 46) A simulation model includes: I. a description of the components of the system. II. a simulation clock. III. a definition of the state of the system. A) I only. B) II only. C) III only. D) I, II, and III. E) I and II only. 47) Which of the following can be used for computer simulation? A) Spreadsheets B) Programming languages C) Simulation languages D) Simulators E) All of the answers choices are correct. 7 Copyright © 2019 McGraw-Hill

48) You have been asked to simulate the process of "flipping" two identical, unbiased coins. How many possible outcomes exist for this process? (Hint: Once the coins are flipped it is impossible to tell which is which.) A) 1 B) 2 C) 3 D) 4 E) 5 49) You have been asked to simulate the process of "flipping" two identical, unbiased coins. What is the probability of the outcome where one coin is heads and the other is tails? (Hint: Once the coins are flipped it is impossible to tell which is which.) A) 0.10 B) 0.25 C) 0.45 D) 0.50 E) 0.75 50) After some experimentation, you have determined that you have a biased coin. The probability of heads is 0.6 and the probability of tails is 0.4. What is the probability that you will observed heads on three successive flips? A) 0.6 B) 0.36 C) 0.24 D) 0.216 E) 0.096 51) After some experimentation, you have determined that you have a biased coin. The probability of heads is 0.6 and the probability of tails is 0.4. If you flip this coin 25 times, how many times would you expect to observe the result "tails"? A) 1 B) 5 C) 10 D) 15 E) 20

52) After reviewing past history, you have assembled the following table showing the frequency of certain levels of sales over the past 40 months. If the smallest random number used to represent sales of 100 units is 0, what will be the largest number used to represent sales of 100 units? Sales (units) 100 150 200 250 300

Frequency 12 6 8 4 10

Corresponding Random Numbers 0 ≤ x < ??

A) 0.1000 B) 0.3000 C) 0.5000 D) 0.7500 E) 0.9000 53) After reviewing past history, you have assembled the following table showing the frequency of certain levels of sales over the past 40 months. If the smallest random number used to represent sales of 200 units is 0.45, what will be the largest number used to represent sales of 200 units? Sales (units) 100 150 200 250 300

Frequency

Corresponding Random Numbers 12 6 8 4 10

A) 0.1000 B) 0.3000 C) 0.5000 D) 0.6500 E) 0.9000

0.45 ≤ x < ??

54) After reviewing past history, you have assembled the following table showing the frequency of certain levels of sales over the past 40 months. If the largest random number used to represent sales of 300 units is 1.00, what will be the smallest number used to represent sales of 300 units? Sales (units) 100 150 200 250 300

Frequency

Corresponding Random Numbers 12 6 8 4 10

?? ≤ x ≤ 1

A) 0.1000 B) 0.3000 C) 0.5000 D) 0.6500 E) 0.7500 55) You have determined that waiting times at a toll booth are uniformly distributed over the interval 20 to 60 seconds. What formula would you use in Excel to generate random values in this range that follow the uniform distribution? A) = (60 − 20) × RAND() B) = (60 + 20) × RAND() C) = 20 + (60 − 20) × RAND() D) = 60 + (60 − 20) × RAND() E) = 20 + (60 + 20) × RAND() 56) You have determined that waiting times at a toll booth are uniformly distributed over the interval 20 to 60 seconds. The first random number your simulation returns is 0.4732. What is the waiting time that this random number generates? A) 38.928 seconds B) 48.928 seconds C) 68.928 seconds D) 78.928 seconds E) 88.928 seconds 57) You have determined that waiting times at a restaurant are uniformly distributed over the interval 5 to 12 minutes. What formula would you use in Excel to generate random values in this range that follow the uniform distribution? A) = (12 − 5 ) × RAND(). B) = (12 + 5 ) × RAND(). C) = 5 + (12 + 5 ) × RAND(). D) = 12 + (12 − 5 ) × RAND(). E) = 5 + (12 − 5 ) × RAND().

58) You have determined that waiting times at a restaurant are uniformly distributed over the interval 5 to 12 minutes. The first random number your simulation returns is 0.2154. What is the waiting time that this random number generates? A) 5 minutes B) 6.5 minutes C) 7.5 minutes D) 10 minutes E) 11 minutes 59) In a model of a stochastic system, the simulation clock is mainly used to A) determine how much computer time to use for the simulation. B) determine how fast the computer can run the simulation. C) determine the amount of simulated time that has elapsed at any point in the simulation. D) estimate how long the simulation will run. E) measure the number of events that will happen during the simulation. 60) The "next-event time advance" procedure does which of the following? I. Determines which upcoming event will occur first. II. Advances the time of the simulation to the next event time. III. Generates a random variable to select the next event which will happen. A) I only B) II only C) III only D) I and II only E) II and III only 61) Which of the following statements about simplifying assumptions in simulations is TRUE? I. Simplifying assumptions should not be used in simulations. II. Simplifying assumptions should lead to conservative estimates. III. Simplifying assumptions should lead to optimistic estimates. A) I only B) II only C) III only D) I and II only E) II and III only 62) Which of the following is NOT a step in the process of conducting a simulation study? A) Collect the data and formulate the simulation model. B) Check the accuracy of the simulation model. C) Plan the simulations to be performed. D) Present recommendations to management. E) All of the answers choices are steps in the simulation process.

63) You are reviewing a simulation model and find that the analyst who prepared the model used the formula = 15 + (45 − 15) × RAND() to generate the simulated cost of a product. Which of the following assumptions did the analyst make about the cost of the product? I. The minimum cost of the product is 15. II. The maximum cost of the product is 60. III. The cost of the product is uniformly distributed. A) I only B) II only C) III only D) I and II only E) I and III only 64) You are reviewing a simulation model and find that the analyst who prepared the model used the formula = 100 + (175 − 100) × RAND() to generate the simulated selling price of a product. Which of the following assumptions did the analyst make about the selling price of the product? I. The minimum price of the product is 175. II. The maximum price of the product is 175. III. The cost of the product is normally distributed. A) I only B) II only C) III only D) I and II only E) I and III only 65) You are reviewing a simulation model and find that the analyst who prepared the model used the formula =NORM.INV(RAND(),100,5) to generate the waiting time at a restaurant (in seconds). Which of the following assumptions did the analyst make about the waiting time? I. The minimum waiting time is 100. II. The average (mean) waiting time is 100. III. The waiting time is normally distributed. A) I only B) II only C) III only D) I and II only E) II and III only

66) You are reviewing a simulation model and find that the analyst who prepared the model used the formula =NORM.INV(RAND(),50,3) to generate the cost of a product. Which of the following assumptions did the analyst make about the product cost? I. The minimum cost is 50. II. The average (mean) cost is 50. III. The cost is uniformly distributed. A) I only B) II only C) III only D) I and II only E) II and III only 67) Customers arrive at a carwash with on average once every 20 minutes. It seems likely that customer arrivals follow an exponential distribution. In a simulation, what formula would you use to estimate how long it will be until the next arrival occurs? A) = 20 + (20 − 0) × RAND() B) = NORM.INV(RAND(),20,3) C) = NORM.INV(RAND(),20,0) D) = 20 × LN(RAND()) E) = − 20 × LN(RAND()) 68) Customers arrive at a carwash with on average once every 20 minutes. It seems likely that customer arrivals follow an exponential distribution. In a simulation, the random number 0.1398 is generated. How long it will be until the next simulated arrival occurs? A) 49.35 minutes B) 39.35 minutes C) 29.35 minutes D) 19.35 minutes E) 9.35 minutes 69) Service times at a doctor's office take an average of 40 minutes. It seems likely that service times follow an exponential distribution. In a simulation, what formula would you use to estimate how long the next service will take? A) = 40 + (40 − 0) × RAND() B) = NORM.INV(RAND(),40,4) C) = NORM.INV(RAND(),40,0) D) = − 40 × LN(RAND()) E) = 40 × LN(RAND()) 70) Service times at a doctor's office take an average of 40 minutes. It seems likely that service times follow an exponential distribution. In a simulation, the random number 0.7588 is generated. How long it will be until the next simulated arrival occurs? A) 1 minute B) 6 minutes C) 11 minutes D) 16 minutes E) 21 minutes 13 Copyright © 2019 McGraw-Hill

A) 10.0 seconds B) 12.0 seconds C) 15.0 seconds D) 18.0 seconds E) 20.0 seconds

74) The Queueing Simulator returned the results shown below for a system with 3 servers. If the firm would like their waiting room to be full no more than 2% of the time, how large must their waiting room be?

A) 4 customers B) 5 customers C) 6 customers D) 7 customers E) 8 customers 75) Note: This question requires the use of the Queueing Simulator spreadsheet in Excel. Use the queueing simulator to simulate a queueing system with 2 servers, exponential interarrival times with a mean of 20 seconds and constant service times of 35 seconds. Use a simulation run length of 10,000 arrivals. What is the point estimate for the average number of customers in the system? A) 2 customers B) 4 customers C) 8 customers D) 9 customers E) 10 customers 76) Note: This question requires the use of the Queueing Simulator spreadsheet in Excel. Use the queueing simulator to simulate a queueing system with 2 servers, exponential interarrival times with a mean of 20 seconds and constant service times of 35 seconds. Use a simulation run length of 10,000 arrivals. If you observe the system at a random time, what is the probability that there will be 3 or more customers waiting in line? A) 0.2 B) 0.4 C) 0.7 D) 0.9 E) 0.99 15 Copyright © 2019 McGraw-Hill

77) The Queueing Simulator returned the results shown below. Which of the following waiting times in the queue is most likely to occur?

A) 60 seconds B) 80 seconds C) 90 seconds D) 100 seconds E) 120 seconds 78) The Queueing Simulator returned the results shown below for a system with 2 servers. Which of the following is most likely to occur?

A) A queue waiting time of 40 seconds. B) A total time in system of 80 seconds. C) A queue length of 5 customers. D) A total of 5 customers in the system. E) All are equally likely. 79) Over the course of an eight hour day, a business normally has about 200 customers arrive. Assuming that the customers arrive at about the same rate over the entire day, what is the interarrival time? A) 1.2 minutes B) 2.0 minutes C) 2.4 minutes D) 3.0 minutes E) 3.6 minutes

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 12 Computer Simulation: Basic Concepts 1) Managers can use simulation to obtain optimal answers for a wide range of problems. Answer: FALSE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the basic concept of computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) Computers can simulate years of operation in seconds. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the basic concept of computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) Simulation is basically an optimizing technique. Answer: FALSE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) Simulation models are fairly easy to use and understand; therefore they can be used for a wide range of decisions. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the basic concept of computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

5) A stochastic system is one that evolved over time according to a continuous probability distribution. Answer: FALSE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the basic concept of computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) When dealing with relatively complex systems, computer simulation is an inexpensive option for decision makers. Answer: FALSE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the basic concept of computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) Simulation is especially useful for situations too complex to be analyzed using analytical models. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) Simulation enables a decision maker to experiment with a system and observe its behavior. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

9) A simulation model is validated if it adequately depicts real system performance. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) One purpose of running experiments on a simulation model is to answer "what-if" questions. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) Simulation is often the first choice of decision makers instead of analytic models. Answer: FALSE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) A number is a random number between 0 and 1 if it is generated in such a way that every possible number within this interval has an equal chance of occurring. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) When using a random number table, it is important to always start at the same point of the table so that results may be replicated. Answer: FALSE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) Random numbers can be generated in Excel by using the VLOOKUP function. Answer: FALSE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) Computer simulation is a useful tool because it generates accurate information using very small samples. Answer: FALSE Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) Random observations can be generated in Excel by using the VLOOKUP function. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

17) Computer simulation is only applicable to situations that have elements that can be described by random variables Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) Analytical methods are preferable to simulation if an appropriate analytic method is available. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) A simulation model includes a description of the components of the system that is to be simulated. Answer: TRUE Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Describe the basic concept of computer simulation. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) A simulation clock keeps track of how long the simulation has run in real time. Answer: FALSE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

21) The main procedure for advancing the time on the simulation clock is called next-event time advance. Answer: TRUE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) Simulation will often give measures of performance as outputs. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) It is always necessary to test the validity of a simulation model by comparing its results with those of an analytic study. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 24) With the speed of computers, it is not necessary to limit the amount of factors considered in a simulation. Answer: FALSE Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Outline the steps of a major computer simulation study. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

25) A simulation model is often formulated in terms of a flow diagram. Answer: TRUE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Outline the steps of a major computer simulation study. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) A flow diagram shows the output of a simulation run. Answer: FALSE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Outline the steps of a major computer simulation study. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) Animation can be used to display computer simulations in action. Answer: TRUE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 28) A larger confidence interval is desirable for a measure of performance since it shows that the results are valid over a larger range. Answer: FALSE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Outline the steps of a major computer simulation study. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

29) One key advantage of computer simulation is that is makes full use of the simplifying approximations that are available. Answer: FALSE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) A parameter analysis report is used to generate many replications of a computer simulation. Answer: FALSE Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) A Data Table can be used to "trick" Excel to perform many replications of a computer simulation. Answer: TRUE Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

32) Given this frequency distribution, the random number 0.2258 would be interpreted as a demand of: Demand 0 1 2 3

Frequency 38 22 22 18

A) 0. B) 1. C) 2. D) 3. E) 1 or 2. Answer: A Explanation: The frequencies of each event can be used to calculate the probability of each event by dividing the frequency of each event by the total of all observations.

The results are then used to determine the corresponding random numbers to each event. A random number of 0.2258 falls within the range for demand of 0.

Demand Frequency Probability 0 38 0.38 1 22 0.22 2 22 0.22 3 18 0.18

Corresponding Random Numbers 0 ≤ x ≤ 0.38 0.38 < x ≤ 0.60 0.60 < x ≤ 0.82 0.82 < x ≤ 1.00

33) Given this frequency distribution, the random number 0.5211 would be interpreted as a demand of: Demand 0 1 2 3

Frequency 38 22 22 18

A) 0. B) 1. C) 2. D) 3. E) 1 or 2. Answer: B Explanation: The frequencies of each event can be used to calculate the probability of each event by dividing the frequency of each event by the total of all observations.

The results are then used to determine the corresponding random numbers to each event. A random number of 0. 5211 falls within the range for demand of 1.

Demand Frequency Probability 0 38 0.38 1 22 0.22 2 22 0.22 3 18 0.18

Corresponding Random Numbers 0 ≤ x ≤ 0.38 0.38 < x ≤ 0.60 0.60 < x ≤ 0.82 0.82 < x ≤ 1.00

34) Given this frequency distribution, the random number 0.9015 would be interpreted as a demand of: Demand 0 1 2 3

Frequency 38 22 22 18

A) 0. B) 1. C) 2. D) 3. E) 1 or 2. Answer: D Explanation: The frequencies of each event can be used to calculate the probability of each event by dividing the frequency of each event by the total of all observations.

The results are then used to determine the corresponding random numbers to each event. A random number of 0.9015 falls within the range for demand of 3.

Demand Frequency Probability 0 38 0.38 1 22 0.22 2 22 0.22 3 18 0.18

Corresponding Random Numbers 0 ≤ x ≤ 0.38 0.38 < x ≤ 0.60 0.60 < x ≤ 0.82 0.82 < x ≤ 1.00

35) The main reason that a large number of replications of a simulation would be made is: A) computers are usually used, and they can easily handle a large number of replications. B) it is part of the scientific approach. C) it is a form of sampling, and large samples give more accurate results than small samples. D) it is more likely to provide optimal answers. E) None of the answer choices is correct. Answer: C Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 36) In order to generate more accurate results when using simulation: A) use a continuous distribution instead of a discreet distribution. B) increase the number of replications. C) increase the number of factors considered. D) All of the answers choices are correct. E) None of the answer choices is correct. Answer: B Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

37) Which of the following would not be a probable reason for choosing simulation as a decision-making tool? A) The situation is too complex for a mathematical model. B) There is a limited time in which to obtain results. C) Good results have been obtained in the past using simulation. D) Users are able to understand the model. E) All of these are probable reasons for choosing simulation. Answer: B Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) Which of the following is not a reason for simulation's popularity? A) It is simple to use and/or understand. B) Extensive software packages are available. C) Many situations are too complex for mathematical solutions. D) If can be used for a wide range of applications. E) It is typically an inexpensive approach. Answer: E Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Describe the role computer simulation plays in many management science studies. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

39) If a simulation begins with the first random number, the first simulated value would be: Random numbers: 0.6246, 0.2594, 0.4055 Demand 0 1 2 3 4

Frequency 0.15 0.30 0.25 0.15 0.15

A) 0. B) 1. C) 2. D) 3. E) 4. Answer: C Explanation: A random number of 0.6246 falls within the range for demand of 2. Demand 0 1 2 3 4

Probability 0.15 0.30 0.25 0.15 0.15

Corresponding Random Numbers 0 ≤ x ≤ 0.15 0.15 < x ≤ 0.45 0.45 < x ≤ 0.70 0.70 < x ≤ 0.85 0.85 < x ≤ 1.00

40) If a simulation begins with the first random number, the second simulated value would be: Random numbers: 0.6246, 0.2594, 0.4055 Demand 0 1 2 3 4

Frequency 0.15 0.30 0.25 0.15 0.15

A) 0. B) 1. C) 2. D) 3. E) 4. Answer: B Explanation: A random number of 0.2594 falls within the range for demand of 1. Demand 0 1 2 3 4

Probability 0.15 0.30 0.25 0.15 0.15

Corresponding Random Numbers 0 ≤ x ≤ 0.15 0.15 < x ≤ 0.45 0.45 < x ≤ 0.70 0.70 < x ≤ 0.85 0.85 < x ≤ 1.00

41) If a simulation begins with the first random number, the third simulated value would be: Random numbers: 0.6246, 0.2594, 0.4055 Demand 0 1 2 3 4

Frequency 0.15 0.30 0.25 0.15 0.15

A) 0. B) 1. C) 2. D) 3. E) 4. Answer: B Explanation: A random number of 0.4055 falls within the range for demand of 1. Demand 0 1 2 3 4

Probability 0.15 0.30 0.25 0.15 0.15

Corresponding Random Numbers 0 ≤ x ≤ 0.15 0.15 < x ≤ 0.45 0.45 < x ≤ 0.70 0.70 < x ≤ 0.85 0.85 < x ≤ 1.00

42) A manager is simulating the number of times a machine operator stops a machine to make adjustments. After careful study the manager found that the number of stops ranged from one to five per cycle and that each number of stops was equally likely. Using the random numbers 0.1835 and 0.3094 (in that order), the next two simulated cycles would respectively have stops for adjustment of: A) 2 and 2. B) 1 and 2. C) 2 and 1. D) 1 and 1. E) 2 and 3. Answer: B Explanation: A random number of 0.1835 falls within the range for demand of 1. A random number of 0.3094 falls within the range for demand of 2. Demand 1 2 3 4 5

Probability 0.20 0.20 0.20 0.20 0.20

Corresponding Random Numbers 0 ≤ x ≤ 0.20 0.20 < x ≤ 0.40 0.40 < x ≤ 0.60 0.60 < x ≤ 0.80 0.80 < x ≤ 1.00

Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 43) Which of the following would not be considered a main advantage of simulation? A) It permits experimentation with the system. B) It generates an optimal solution. C) It compresses time. D) It can serve as a training tool. E) All of the answers choices are advantages. Answer: B Difficulty: 1 Easy Topic: The Essence of Computer Simulation Learning Objective: Describe the basic concept of computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

44) On cold mornings, the probability that David's car won't start is 0.22. When it doesn't start, he takes the bus and is late for work. When it does start, he drives to work on the freeway. Sixty-five percent of the time the freeway is clear, and he gets to work on time. The rest of the time he is late. Simulate 10 consecutive days' worth of trips to work using the random numbers given (use the smaller numbers to represent "car won't start" and "freeway clear"). Random numbers: Car 0.7772 0.2902 0.8120 0.2259 0.0527 0.2958 0.2891 0.0131 0.5219 0.9949

Traffic 0.2282 0.3674 0.1654 0.6909 0.7010 0.9802 0.5615 0.5604 0.4361 0.1405

How many times is David late for work because his car won't start? A) 0. B) 1. C) 2. D) 3. E) 4. Answer: C Explanation: Using a probability of less than 0.22 as indicating the car did not start, two values (0.0527 and 0.0131) indicate that David's car did not start. Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Traffic 0.2282 0.3674 0.1654 0.6909 0.7010 0.9802 0.5615 0.5604 0.4361 0.1405

How many times is David late for work? A) 1. B) 2. C) 3. D) 4. E) 5.

Answer: E Explanation: David will be late for work unless his car starts and traffic is clear the same day. In this case, he will be late for work on 5 days. Day

Car 1 0.7772 2 0.2902 3 0.8120 4 0.2259 5 0.0527 6 0.2958 7 0.2891 8 0.0131 9 0.5219 10 0.9949

Traffic 0.2282 0.3674 0.1654 0.6909 0.7010 0.9802 0.5615 0.5604 0.4361 0.1405

Car Start Freeway Clear On-Time Yes No No Yes Yes Yes Yes No No Yes Yes Yes No Yes No Yes Yes Yes Yes Yes Yes No Yes No Yes Yes Yes Yes No No

Difficulty: 3 Hard Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 46) A simulation model includes: I. a description of the components of the system. II. a simulation clock. III. a definition of the state of the system. A) I only. B) II only. C) III only. D) I, II, and III. E) I and II only. Answer: D Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

47) Which of the following can be used for computer simulation? A) Spreadsheets B) Programming languages C) Simulation languages D) Simulators E) All of the answers choices are correct. Answer: E Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Outline the steps of a major computer simulation study. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 48) You have been asked to simulate the process of "flipping" two identical, unbiased coins. How many possible outcomes exist for this process? (Hint: Once the coins are flipped it is impossible to tell which is which.) A) 1 B) 2 C) 3 D) 4 E) 5 Answer: C Explanation: Each coin can end up as heads (H) or tails (T). With two coins, the possible results are H-H, H-T, T-H, or TT. However, since it isn't possible to tell which coin is which, H-T and T-H are the same thing, so the result H-T and T-H are the same, leading to three possible outcomes (H-H, H-T, and T-T). Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

49) You have been asked to simulate the process of "flipping" two identical, unbiased coins. What is the probability of the outcome where one coin is heads and the other is tails? (Hint: Once the coins are flipped it is impossible to tell which is which.) A) 0.10 B) 0.25 C) 0.45 D) 0.50 E) 0.75 Answer: D Explanation: Each coin can end up as heads (H) or tails (T). With two coins, the possible results are H-H, H-T, T-H, or TT. However, since it isn't possible to tell which coin is which, H-T and T-H are the same thing, so the result H-T and T-H are the same, leading to three possible outcomes (H-H, H-T, and T-T). However, there are two paths to the outcome H-T. H-T has a probability of 0.25 (0.5 x 0.5) and T-H also has a probability of 0.25 (0.5 x 0.5). The sum of the probabilities of these two paths is 0.5. Difficulty: 3 Hard Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 50) After some experimentation, you have determined that you have a biased coin. The probability of heads is 0.6 and the probability of tails is 0.4. What is the probability that you will observed heads on three successive flips? A) 0.6 B) 0.36 C) 0.24 D) 0.216 E) 0.096 Answer: D Explanation: Since the probability of heads is 0.6, the probability of three heads successively is the product of the individual probabilities. 0.6 × 0.6 × 0.6 = 0.216. Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

51) After some experimentation, you have determined that you have a biased coin. The probability of heads is 0.6 and the probability of tails is 0.4. If you flip this coin 25 times, how many times would you expect to observe the result "tails"? A) 1 B) 5 C) 10 D) 15 E) 20 Answer: C Explanation: Since the probability of tails is 0.4, the expected number of tails is the probability of the event times the number of trials (0.4 × 25 = 10). Difficulty: 2 Medium Topic: The Essence of Computer Simulation Learning Objective: Use random numbers to generate random events that have a simple discrete distribution. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

Frequency 12 6 8 4 10

Corresponding Random Numbers 0 ≤ x < ??

A) 0.1000 B) 0.3000 C) 0.5000 D) 0.7500 E) 0.9000 Answer: B Explanation: Sales of 100 occurred in 12 out of 40 months. This is a probability of 0.3 (12 / 40 = 0.3). Therefore, if the lower end of the range of random numbers is 0, the upper end of the range will be 0.3. Sales (units) 100 150 200 250 300

Frequency Corresponding Random Numbers 12 0 ≤ x < 0.3000 6 8 4 10

53) After reviewing past history, you have assembled the following table showing the frequency of certain levels of sales over the past 40 months. If the smallest random number used to represent sales of 200 units is 0.45, what will be the largest number used to represent sales of 200 units? Sales (units) 100 150 200 250 300

Frequency

Corresponding Random Numbers 12 6 8 4 10

0.45 ≤ x < ??

A) 0.1000 B) 0.3000 C) 0.5000 D) 0.6500 E) 0.9000 Answer: D Explanation: Sales of 200 occurred in 8 out of 40 months. This is a probability of 0.2 (8 / 40 = 0.2). Therefore, if the lower end of the range of random numbers is 0.45, the upper end of the range will be 0.65 (0.45 + 0.2). Sales (units) 100 150 200 250 300

Frequency Corresponding Random Numbers 12 6 8 0.45 ≤ x < 0.65 4 10

Frequency

Corresponding Random Numbers 12 6 8 4 10

?? ≤ x ≤ 1

A) 0.1000 B) 0.3000 C) 0.5000 D) 0.6500 E) 0.7500 Answer: E Explanation: Sales of 300 occurred in 10 out of 40 months. This is a probability of 0.25 (10 / 40 = 0.25). Therefore, if the upper end of the range of random numbers is 1.00, the lower end of the range will be 0.75 (1.00 − 0.25). Sales (units) 100 150 200 250 300

Frequency Corresponding Random Numbers 12 6 8 4 10 0.75 ≤ x ≤ 1.00

55) You have determined that waiting times at a toll booth are uniformly distributed over the interval 20 to 60 seconds. What formula would you use in Excel to generate random values in this range that follow the uniform distribution? A) = (60 − 20) × RAND() B) = (60 + 20) × RAND() C) = 20 + (60 − 20) × RAND() D) = 60 + (60 − 20) × RAND() E) = 20 + (60 + 20) × RAND() Answer: C Explanation: The formula to generate a uniformly generated variable that ranges between a and b is = a + (b − a) × RAND(). In this case, a = 20 and b = 60, so the formula is = 20 + (60 − 20) × RAND(). Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 56) You have determined that waiting times at a toll booth are uniformly distributed over the interval 20 to 60 seconds. The first random number your simulation returns is 0.4732. What is the waiting time that this random number generates? A) 38.928 seconds B) 48.928 seconds C) 68.928 seconds D) 78.928 seconds E) 88.928 seconds Answer: A Explanation: The formula to generate a uniformly generated variable that ranges between a and b is = a + (b − a) * RAND(). In this case, a = 20 and b = 60, so the formula is = 20 + (60 − 20) * RAND(). With a random number of 0.4732, this leads to a waiting time of 38.928 seconds (20 + (60 − 20) * 0.4732 = 38.928). Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

57) You have determined that waiting times at a restaurant are uniformly distributed over the interval 5 to 12 minutes. What formula would you use in Excel to generate random values in this range that follow the uniform distribution? A) = (12 − 5 ) × RAND(). B) = (12 + 5 ) × RAND(). C) = 5 + (12 + 5 ) × RAND(). D) = 12 + (12 − 5 ) × RAND(). E) = 5 + (12 − 5 ) × RAND(). Answer: E Explanation: The formula to generate a uniformly generated variable that ranges between a and b is = a + (b − a) × RAND(). In this case, a = 5 and b = 12, so the formula is = 5 + (12 − 5 ) × RAND(). Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 58) You have determined that waiting times at a restaurant are uniformly distributed over the interval 5 to 12 minutes. The first random number your simulation returns is 0.2154. What is the waiting time that this random number generates? A) 5 minutes B) 6.5 minutes C) 7.5 minutes D) 10 minutes E) 11 minutes Answer: B Explanation: The formula to generate a uniformly generated variable that ranges between a and b is = a + (b − a) × RAND(). In this case, a = 5 and b = 12, so the formula is = 5 + (12 − 5 ) × RAND(). With a random number of 0.2154, this leads to a waiting time of 6.5 minutes (5 + (12 − 5 ) × 0.2154 = 6.5078). Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

59) In a model of a stochastic system, the simulation clock is mainly used to A) determine how much computer time to use for the simulation. B) determine how fast the computer can run the simulation. C) determine the amount of simulated time that has elapsed at any point in the simulation. D) estimate how long the simulation will run. E) measure the number of events that will happen during the simulation. Answer: C Difficulty: 2 Medium Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 60) The "next-event time advance" procedure does which of the following? I. Determines which upcoming event will occur first. II. Advances the time of the simulation to the next event time. III. Generates a random variable to select the next event which will happen. A) I only B) II only C) III only D) I and II only E) II and III only Answer: D Difficulty: 2 Medium Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

61) Which of the following statements about simplifying assumptions in simulations is TRUE? I. Simplifying assumptions should not be used in simulations. II. Simplifying assumptions should lead to conservative estimates. III. Simplifying assumptions should lead to optimistic estimates. A) I only B) II only C) III only D) I and II only E) II and III only Answer: B Difficulty: 2 Medium Topic: Analysis of the Case Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 62) Which of the following is NOT a step in the process of conducting a simulation study? A) Collect the data and formulate the simulation model. B) Check the accuracy of the simulation model. C) Plan the simulations to be performed. D) Present recommendations to management. E) All of the answers choices are steps in the simulation process. Answer: E Difficulty: 1 Easy Topic: Outline of a Major Computer Simulation Study Learning Objective: Outline the steps of a major computer simulation study. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

63) You are reviewing a simulation model and find that the analyst who prepared the model used the formula = 15 + (45 − 15) × RAND() to generate the simulated cost of a product. Which of the following assumptions did the analyst make about the cost of the product? I. The minimum cost of the product is 15. II. The maximum cost of the product is 60. III. The cost of the product is uniformly distributed. A) I only B) II only C) III only D) I and II only E) I and III only Answer: E Explanation: The analyst used a formula that generates a uniformly distributed cost between 15 and 45. Therefore, I and III are true. Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 64) You are reviewing a simulation model and find that the analyst who prepared the model used the formula = 100 + (175 − 100) × RAND() to generate the simulated selling price of a product. Which of the following assumptions did the analyst make about the selling price of the product? I. The minimum price of the product is 175. II. The maximum price of the product is 175. III. The cost of the product is normally distributed. A) I only B) II only C) III only D) I and II only E) I and III only Answer: B Explanation: The analyst used a formula that generates a uniformly distributed cost between 100 and 175. Therefore, only II is true. Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

65) You are reviewing a simulation model and find that the analyst who prepared the model used the formula =NORM.INV(RAND(),100,5) to generate the waiting time at a restaurant (in seconds). Which of the following assumptions did the analyst make about the waiting time? I. The minimum waiting time is 100. II. The average (mean) waiting time is 100. III. The waiting time is normally distributed. A) I only B) II only C) III only D) I and II only E) II and III only Answer: E Explanation: The analyst used a formula that generates a normally distributed waiting time with a mean of 100 and a standard deviation of 5. Therefore, II and III are true. Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 66) You are reviewing a simulation model and find that the analyst who prepared the model used the formula =NORM.INV(RAND(),50,3) to generate the cost of a product. Which of the following assumptions did the analyst make about the product cost? I. The minimum cost is 50. II. The average (mean) cost is 50. III. The cost is uniformly distributed. A) I only B) II only C) III only D) I and II only E) II and III only Answer: B Explanation: The analyst used a formula that generates a normally distributed cost with a mean of 50 and a standard deviation of 3. Therefore, only II is true. Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

67) Customers arrive at a carwash with on average once every 20 minutes. It seems likely that customer arrivals follow an exponential distribution. In a simulation, what formula would you use to estimate how long it will be until the next arrival occurs? A) = 20 + (20 − 0) × RAND() B) = NORM.INV(RAND(),20,3) C) = NORM.INV(RAND(),20,0) D) = 20 × LN(RAND()) E) = − 20 × LN(RAND()) Answer: E Explanation: To simulate an exponential distribution, use the natural logarithm formula in Excel. In this case, the correct formula is = −20 × LN(RAND()). Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 68) Customers arrive at a carwash with on average once every 20 minutes. It seems likely that customer arrivals follow an exponential distribution. In a simulation, the random number 0.1398 is generated. How long it will be until the next simulated arrival occurs? A) 49.35 minutes B) 39.35 minutes C) 29.35 minutes D) 19.35 minutes E) 9.35 minutes Answer: B Explanation: To simulate an exponential distribution, use the natural logarithm formula in Excel. In this case, the correct formula is = −20 × LN(RAND()). With a random number of 0.1398, this equation returns an arrival time of 39.35 minutes. Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation

69) Service times at a doctor's office take an average of 40 minutes. It seems likely that service times follow an exponential distribution. In a simulation, what formula would you use to estimate how long the next service will take? A) = 40 + (40 − 0) × RAND() B) = NORM.INV(RAND(),40,4) C) = NORM.INV(RAND(),40,0) D) = − 40 × LN(RAND()) E) = 40 × LN(RAND()) Answer: D Explanation: To simulate an exponential distribution, use the natural logarithm formula in Excel. In this case, the correct formula is = −40 × LN(RAND()). Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Evaluate AACSB: Analytical Thinking Accessibility: Keyboard Navigation 70) Service times at a doctor's office take an average of 40 minutes. It seems likely that service times follow an exponential distribution. In a simulation, the random number 0.7588 is generated. How long it will be until the next simulated arrival occurs? A) 1 minute B) 6 minutes C) 11 minutes D) 16 minutes E) 21 minutes Answer: C Explanation: To simulate an exponential distribution, use the natural logarithm formula in Excel. In this case, the correct formula is = −40 × LN(RAND()).With a random number of 0.7588, this equation returns an arrival time of 11.04 minutes. Difficulty: 3 Hard Topic: A Case Study: Herr Cutter's Barber Shop (Revisited) Learning Objective: Use Excel to perform basic computer simulations on a spreadsheet. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

71) Note: This question requires the use of the Queueing Simulator spreadsheet in Excel. Use the queueing simulator to simulate a queueing system with 3 servers, uniform interarrival times between 20 and 50 seconds and exponential service times with an average of 75 seconds. Use a simulation run length of 10,000 arrivals. What is the point estimate for the total amount of time a customer will spend in the system? A) 75 seconds B) 90 seconds C) 105 seconds D) 120 seconds E) 135 seconds Answer: B Explanation: The Queueing Simulator returns a total time in the system (W) of about 90 seconds. Your value may vary somewhat due to the use of the random number generator. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 72) Note: This question requires the use of the Queueing Simulator spreadsheet in Excel. Use the queueing simulator to simulate a queueing system with 3 servers, uniform interarrival times between 20 and 50 seconds and exponential service times with an average of 75 seconds. Use a simulation run length of 10,000 arrivals. If you observe the system at a random time, what is the probability that there will be 4 or more customers waiting in line? A) 0.2 B) 0.4 C) 0.6 D) 0.8 E) 0.9 Answer: A Explanation: The Queueing Simulator returns the following probabilities for 0 to 3 customers in the system (P(0) = 0.0435, P(1) = 0.2037, P(2) = 0.3104, P(3) = 0.2171). The probability of 4 or more customers is equal to 1 − P(x < 4), so P(x ≥ 4) = 0.2252. Your value may vary somewhat due to the use of the random number generator. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation

73) The Queueing Simulator returned the results shown below. Which of the following waiting times in the queue is most likely to occur?

A) 10.0 seconds B) 12.0 seconds C) 15.0 seconds D) 18.0 seconds E) 20.0 seconds Answer: C Explanation: The Queueing Simulator returned a total time in the queue (Wq) range of about 15.3 to 17.3 seconds (95% confidence interval). The only choice that falls within this range is c, 15 seconds. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation

A) 4 customers B) 5 customers C) 6 customers D) 7 customers E) 8 customers Answer: A Explanation: The Queueing Simulator results indicate that there will be 7 or fewer customers in the system with a probability of 0.9836. With three servers (and therefore up to 3 customers in service), this indicates a need for a waiting room that will hold 4 customers. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation

75) Note: This question requires the use of the Queueing Simulator spreadsheet in Excel. Use the queueing simulator to simulate a queueing system with 2 servers, exponential interarrival times with a mean of 20 seconds and constant service times of 35 seconds. Use a simulation run length of 10,000 arrivals. What is the point estimate for the average number of customers in the system? A) 2 customers B) 4 customers C) 8 customers D) 9 customers E) 10 customers Answer: B Explanation: The Queueing Simulator returns a total time in the system (L) of about 4 customers. Your value may vary somewhat due to the use of the random number generator. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 76) Note: This question requires the use of the Queueing Simulator spreadsheet in Excel. Use the queueing simulator to simulate a queueing system with 2 servers, exponential interarrival times with a mean of 20 seconds and constant service times of 35 seconds. Use a simulation run length of 10,000 arrivals. If you observe the system at a random time, what is the probability that there will be 3 or more customers waiting in line? A) 0.2 B) 0.4 C) 0.7 D) 0.9 E) 0.99 Answer: C Explanation: The Queueing Simulator returns the following probabilities for 0 to 2 customers in the system (P(0) = 0.05, P(1) = 0.12, P(2) = 0.14). The probability of 3 or more customers is equal to 1 − P(x < 2), so P(x ≥ 3) = 0.69. Your value may vary somewhat due to the use of the random number generator. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation

77) The Queueing Simulator returned the results shown below. Which of the following waiting times in the queue is most likely to occur?

A) 60 seconds B) 80 seconds C) 90 seconds D) 100 seconds E) 120 seconds Answer: A Explanation: The Queueing Simulator returned a total time in the queue (Wq) range of about 50 to 72 seconds (95% confidence interval). The only choice that falls within this range is a, 60 seconds. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation

78) The Queueing Simulator returned the results shown below for a system with 2 servers. Which of the following is most likely to occur?

A) A queue waiting time of 40 seconds. B) A total time in system of 80 seconds. C) A queue length of 5 customers. D) A total of 5 customers in the system. E) All are equally likely. Answer: C Explanation: According to the Queueing Simulator results, only a total of 5 customers in the system (L = 5) falls within the 95% confidence intervals. Difficulty: 2 Medium Topic: Outline of a Major Computer Simulation Study Learning Objective: Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation

79) Over the course of an eight hour day, a business normally has about 200 customers arrive. Assuming that the customers arrive at about the same rate over the entire day, what is the interarrival time? A) 1.2 minutes B) 2.0 minutes C) 2.4 minutes D) 3.0 minutes E) 3.6 minutes Answer: C Explanation: 200 customers in eight hours is a rate of 0.417 customers per minute time is the reciprocal of the arrival rate

The interarrival

Difficulty: 3 Hard Topic: Analysis of the Case Study Learning Objective: Describe and use the building blocks of a simulation model for a stochastic system. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 13 Computer Simulation with Analytic Solver 1) A results cell refers to a random input cell. 2) The number of trials is one of the options to be set in RSPE. 3) The distribution used for the uncertain variable cells is one of the options to be set in the Simulation Options in RSPE. 4) Increasing the number of trials increases the accuracy of a simulation. 5) The standard error gives an indication of the accuracy of the estimated mean. 6) The sensitivity chart in RSPE indicates the increase in the results cell per unit increase in the uncertain variable cell. 7) The sensitivity chart in RSPE indicates how strongly various uncertain variable cells influence the results cell. 8) The normal distribution is a good choice when all values within a range are equally likely. 9) The triangular distribution has a fixed upper and lower bound. 10) The normal distribution has a fixed upper and lower bound. 11) A danger of using the lognormal distribution is that values can fall below zero. 12) A danger of using the normal distribution is that values can fall below zero. 13) The exponential distribution is widely used to describe the time between random events. 14) The geometric distribution describes the number of times an event occurs in a fixed number of trials. 15) The binomial distribution describes the number of times an event occurs in a fixed number of trials. 16) The negative binomial distribution describes the number of trials until an event occurs n times. 17) The custom distribution in RSPE allows only discrete distributions to be entered. 18) RSPE can be used to fit a discrete distribution to data. 19) RSPE can be used to fit a continuous distribution to data. 20) The parameter analysis report in RSPE can be used to systematically investigate a set of values for a decision variable in a simulation model. 1 Copyright © 2019 McGraw-Hill

21) The more trials that are run, the lower the standard error will become. 22) A trend chart shows the trend in profit values from trial to trial. 23) RSPE is guaranteed to find the optimal solution to a simulation problem. 24) RSPE cannot handle constraints in a simulation model. 25) The PERT method for project management assumes that task durations follow a triangular distribution. 26) The PERT method for project management assumes that task durations follow a beta distribution. 27) Computer simulations of project management problems often use a triangular distribution to represent the task durations in a project management problem. 28) The normal distribution is a good choice to represent the task durations in a project management problem. 29) The use of different hotel rates for different classes of customers is known as revenue management. 30) The ride sharing firm Uber uses dynamic pricing, which results in higher fares during busy times and lower fares during less busy times. This is an example of revenue management. 31) A grocery chain has decided to reduce the price of milk to encourage customers to purchase higher quantities. This is an example of revenue management. 32) A central-tendency distribution is likely to have two separate peaks, indicating that two widely separated sets of values are equally likely. 33) A probability distribution shows the relative likelihood of observing any particular value. 34) The normal distribution is popular because it accurately portrays the variation observed in natural phenomenon. 35) If an analyst knows the minimum and maximum values possible for a parameter, the triangular distribution is a good choice for modeling. 36) The triangular distribution is always a symmetric distribution. 37) The normal distribution is always a symmetric distribution. 38) If the mean value of a parameter is known, it is possible to use the normal distribution to model the parameter. 2 Copyright © 2019 McGraw-Hill

39) Which of the following is not a step required to perform a simulation with RSPE? A) Define the uncertain variable cells. B) Define the results cells to forecast. C) Set the simulation options. D) Develop the spreadsheet model. E) All are steps required to perform a simulation with RSPE. 40) Which of the following is a random input cell in RSPE? A) An uncertain variable cell. B) A decision variable. C) A results cell. D) A statistic cell. E) None of the answer choices is correct. 41) The cell that represents the output of a computer simulation is referred to as: A) an uncertain variable cell. B) a decision variable. C) a results cell. D) a statistic cell. E) None of the answer choices is correct. 42) A distribution is chosen from the Distributions menu for which type of cell? A) An uncertain variable cell B) A decision variable C) A results cell D) A statistic cell E) None of the answer choices is correct. 43) Which of the following charts shows a histogram giving the relative frequency of the various output values in the forecast cell? A) Frequency chart B) Statistics table C) Percentiles table D) Cumulative frequency chart E) Reverse cumulative chart 44) Which of the following provide the mean, median, standard deviation, range, etc. for the results cell in RSPE? A) Frequency chart B) Statistics table C) Percentiles table D) Cumulative frequency chart E) None of the answer choices is correct.

45) When applying simulation to an inventory problem, which of the following would be an uncertain variable cell? A) The total profit B) The holding cost per unit C) The demand D) All of the answers choices are correct. E) None of the answer choices is correct. 46) When applying simulation to an inventory problem, which of the following is the most appropriate choice for the results cell? A) The total profit B) The holding cost per unit C) The demand D) All of the answers choices are correct. E) None of the answer choices is correct. 47) Which of the following are advantages of computer simulation over analytical methods like PERT/CPM for predicting the probability that a project will complete by a deadline? I. It does not need to make as many simplifying assumptions. II. It is more flexible about which probability distributions can be used. III. It provides a solution more quickly. A) I only B) II only C) III only D) I, II, and III E) I and II only 48) The sensitivity chart conveys which of the following? A) The relative frequency of various results cell values B) The increase in profit per unit increase in an uncertain variable cell C) It indicates how strongly various uncertain variable cells influence the results cell D) The mean profit E) None of the answer choices is correct. 49) Which of the following is not one of the charts or tables provided by RSPE? A) Frequency chart B) Statistics table C) Standard error chart D) Cumulative frequency chart E) Percentiles table 50) Which chart indicates the trend in forecast values as a particular decision variable is varied? A) Frequency chart B) Trend chart C) Cumulative frequency chart D) Statistics table E) None of the answer choices is correct. 4 Copyright © 2019 McGraw-Hill

51) Which of the following is not a characteristic of the normal distribution? A) Some value is the most likely. B) Values closest to the mean are more likely. C) It must be symmetric. D) Values cannot fall below zero. E) Extreme values are possible, but rare. 52) Which of the following is not a characteristic of the triangular distribution? A) Some value is the most likely. B) Values close to the most likely value are more common. C) The most likely value is the mean. D) It can be asymmetric. E) It has a fixed upper and lower bound. 53) Which of the following is not a characteristic of the lognormal distribution? A) Some value is the most likely. B) It is negatively skewed (above the mean more likely). C) Values cannot fall below zero. D) Extreme values (high end only) are possible, but rare. E) All of the answers choices are characteristic of the lognormal distribution. 54) Which of the following is not a characteristic of the uniform distribution? A) It has a fixed minimum value B) It has a fixed maximum value C) Some value is the most likely D) All of the answers choices are characteristic of the uniform distribution. E) None of the answers choices is characteristic of the uniform distribution. 55) Which of the following distributions is widely used to describe the time between random events? A) Uniform distribution B) Exponential distribution C) Poisson distribution D) Normal distribution E) None of the answer choices is correct. 56) Which of the following distributions describes the number of times an event occurs during a given period of time or space? A) Uniform distribution B) Exponential distribution C) Poisson distribution D) Normal distribution E) None of the answer choices is correct.

57) Which of the following distributions describes the number of times an event occurs in a fixed number of trials? A) Binomial distribution B) Geometric distribution C) Negative binomial distribution D) Poisson distribution E) None of the answer choices is correct. 58) Which of the following distributions describes the number of trials until an event occurs? A) Binomial distribution B) Geometric distribution C) Negative binomial distribution D) Poisson distribution E) None of the answer choices is correct. 59) Which of the following distributions describes the number of trials until an event occurs n times? A) Binomial distribution B) Geometric distribution C) Negative binomial distribution D) Poisson distribution E) None of the answer choices is correct. 60) The parameter analysis report can simultaneously vary up to how many different decision variables? A) 1 B) 2 C) 3 D) 4 E) Any number of decision variables. 61) The RSPE Solver can be used to simultaneously optimize up to how many decision variables? A) 1 B) 2 C) 3 D) 4 E) Many decision variables can be optimized simultaneously.

62) Which of the following distributions is positively skewed? I. Normal distribution II. Uniform distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only III and IV 63) Which of the following distributions is not skewed? I. Normal distribution II. Uniform distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only I and II 64) Which of the following distributions has a fixed minimum and maximum? I. Normal distribution II. Uniform distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only I and II 65) Which of the following distributions has a fixed minimum and maximum? I. Normal distribution II. Triangular distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only I and II 7 Copyright © 2019 McGraw-Hill

66) Which of the following is NOT a continuous distribution? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution 67) Which of the following is a discrete distribution? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution 68) The relative likelihood of any particular value is given by the height of the distribution's A) central-tendency distribution. B) probability density function. C) cumulative density function. D) most likely value. E) standard deviation. 69) Which of the following is NOT a central-tendency distribution? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Uniform distribution E) Exponential distribution 70) For a distribution that is positively skewed, which of the following is TRUE? A) The mean and the standard deviation are equal. B) The mean will be located to the right of the most likely value. C) The mean will be located to the left of the most likely value. D) All values are equally likely. E) The mean and the most likely value will be the same. 71) Which of the following distributions would be most appropriate for modeling the number of students found in a small classroom? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution

72) The exponential distribution has a most likely value that is equal to A) zero. B) the mean. C) the variance. D) All of the answers choices are true. E) None of the answer choices is true. 73) The distribution shown below is most likely which of the following?

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution

74) The distribution shown below is most likely which of the following?

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution 75) The distribution shown below is most likely which of the following?

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Uniform distribution E) Exponential distribution

76) One way to ensure that Analytic Solver identifies an optimal solution quickly is to do which of the following? I. Set the "Max Time without Improvement" setting to zero. II. Add bounds for the decision variables. III. Add integer constraints to the model. A) I only B) II only C) III only D) Only II and III E) I, II, and III 77) A manager has observed sales for a number of days and developed the following table of probabilities. Which of the following distributions would be most appropriate for modeling the daily sales? Daily Sales 100 200 300 400

Probability 0.40 0.05 0.50 0.05

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Custom discrete distribution

Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 13 Computer Simulation with Analytic Solver 1) A results cell refers to a random input cell. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 2) The number of trials is one of the options to be set in RSPE. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 3) The distribution used for the uncertain variable cells is one of the options to be set in the Simulation Options in RSPE. Answer: FALSE Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 4) Increasing the number of trials increases the accuracy of a simulation. Answer: TRUE Difficulty: 2 Medium Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

5) The standard error gives an indication of the accuracy of the estimated mean. Answer: TRUE Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 6) The sensitivity chart in RSPE indicates the increase in the results cell per unit increase in the uncertain variable cell. Answer: FALSE Difficulty: 1 Easy Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Interpret the results generated by Analytic Solver when performing a computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 7) The sensitivity chart in RSPE indicates how strongly various uncertain variable cells influence the results cell. Answer: TRUE Difficulty: 1 Easy Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Interpret the results generated by Analytic Solver when performing a computer simulation. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 8) The normal distribution is a good choice when all values within a range are equally likely. Answer: FALSE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

9) The triangular distribution has a fixed upper and lower bound. Answer: TRUE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 10) The normal distribution has a fixed upper and lower bound. Answer: FALSE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 11) A danger of using the lognormal distribution is that values can fall below zero. Answer: FALSE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 12) A danger of using the normal distribution is that values can fall below zero. Answer: TRUE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

13) The exponential distribution is widely used to describe the time between random events. Answer: TRUE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 14) The geometric distribution describes the number of times an event occurs in a fixed number of trials. Answer: FALSE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 15) The binomial distribution describes the number of times an event occurs in a fixed number of trials. Answer: TRUE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16) The negative binomial distribution describes the number of trials until an event occurs n times. Answer: TRUE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

17) The custom distribution in RSPE allows only discrete distributions to be entered. Answer: FALSE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 18) RSPE can be used to fit a discrete distribution to data. Answer: TRUE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Use an Analytic Solver procedure that identifies the continuous distribution that best fits historical data. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 19) RSPE can be used to fit a continuous distribution to data. Answer: TRUE Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Use an Analytic Solver procedure that identifies the continuous distribution that best fits historical data. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 20) The parameter analysis report in RSPE can be used to systematically investigate a set of values for a decision variable in a simulation model. Answer: TRUE Difficulty: 1 Easy Topic: Decision Making With Parameter Analysis Reports and Trend Charts Learning Objective: Use Analytic Solver to generate a parameter analysis report and a trend chart as an aid to decision making. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

21) The more trials that are run, the lower the standard error will become. Answer: TRUE Difficulty: 2 Medium Topic: Decision Making With Parameter Analysis Reports and Trend Charts Learning Objective: Use Analytic Solver to generate a parameter analysis report and a trend chart as an aid to decision making. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 22) A trend chart shows the trend in profit values from trial to trial. Answer: FALSE Difficulty: 1 Easy Topic: Decision Making With Parameter Analysis Reports and Trend Charts Learning Objective: Use Analytic Solver to generate a parameter analysis report and a trend chart as an aid to decision making. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 23) RSPE is guaranteed to find the optimal solution to a simulation problem. Answer: FALSE Difficulty: 1 Easy Topic: Optimizing With Computer Simulation Using the Solver in Analytic Solver Learning Objective: Use the Solver in Analytic Solver to search for an optimal solution for a simulation model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 24) RSPE cannot handle constraints in a simulation model. Answer: FALSE Difficulty: 1 Easy Topic: Optimizing With Computer Simulation Using the Solver in Analytic Solver Learning Objective: Use the Solver in Analytic Solver to search for an optimal solution for a simulation model. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

25) The PERT method for project management assumes that task durations follow a triangular distribution. Answer: FALSE Difficulty: 1 Easy Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 26) The PERT method for project management assumes that task durations follow a beta distribution. Answer: TRUE Difficulty: 1 Easy Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 27) Computer simulations of project management problems often use a triangular distribution to represent the task durations in a project management problem. Answer: TRUE Difficulty: 1 Easy Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

28) The normal distribution is a good choice to represent the task durations in a project management problem. Answer: FALSE Explanation: Since the normal distribution includes negative values, it is a poor choice to model task durations. Difficulty: 2 Medium Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 29) The use of different hotel rates for different classes of customers is known as revenue management. Answer: TRUE Difficulty: 1 Easy Topic: Revenue Management in the Travel Industry Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 30) The ride sharing firm Uber uses dynamic pricing, which results in higher fares during busy times and lower fares during less busy times. This is an example of revenue management. Answer: TRUE Difficulty: 2 Medium Topic: Revenue Management in the Travel Industry Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 31) A grocery chain has decided to reduce the price of milk to encourage customers to purchase higher quantities. This is an example of revenue management. Answer: FALSE Difficulty: 2 Medium Topic: Revenue Management in the Travel Industry Learning Objective: Describe the role of Analytic Solver in performing computer simulations. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

32) A central-tendency distribution is likely to have two separate peaks, indicating that two widely separated sets of values are equally likely. Answer: FALSE Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 33) A probability distribution shows the relative likelihood of observing any particular value. Answer: TRUE Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 34) The normal distribution is popular because it accurately portrays the variation observed in natural phenomenon. Answer: TRUE Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 35) If an analyst knows the minimum and maximum values possible for a parameter, the triangular distribution is a good choice for modeling. Answer: FALSE Explanation: The triangular distribution requires knowledge of the minimum, maximum and most likely values. Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 9 Copyright © 2019 McGraw-Hill

36) The triangular distribution is always a symmetric distribution. Answer: FALSE Explanation: The triangular distribution can be symmetric or asymmetric, depending upon the parameters chosen. Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 37) The normal distribution is always a symmetric distribution. Answer: TRUE Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 38) If the mean value of a parameter is known, it is possible to use the normal distribution to model the parameter. Answer: FALSE Explanation: The normal distribution requires knowledge of the mean and the standard deviation. Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

39) Which of the following is not a step required to perform a simulation with RSPE? A) Define the uncertain variable cells. B) Define the results cells to forecast. C) Set the simulation options. D) Develop the spreadsheet model. E) All are steps required to perform a simulation with RSPE. Answer: E Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 40) Which of the following is a random input cell in RSPE? A) An uncertain variable cell. B) A decision variable. C) A results cell. D) A statistic cell. E) None of the answer choices is correct. Answer: A Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 41) The cell that represents the output of a computer simulation is referred to as: A) an uncertain variable cell. B) a decision variable. C) a results cell. D) a statistic cell. E) None of the answer choices is correct. Answer: C Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 11 Copyright © 2019 McGraw-Hill

42) A distribution is chosen from the Distributions menu for which type of cell? A) An uncertain variable cell B) A decision variable C) A results cell D) A statistic cell E) None of the answer choices is correct. Answer: A Difficulty: 1 Easy Topic: A Case Study: Freddie the Newsboy's Problem Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 43) Which of the following charts shows a histogram giving the relative frequency of the various output values in the forecast cell? A) Frequency chart B) Statistics table C) Percentiles table D) Cumulative frequency chart E) Reverse cumulative chart Answer: A Difficulty: 1 Easy Topic: Bidding For a Construction Project: A Prelude to the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

44) Which of the following provide the mean, median, standard deviation, range, etc. for the results cell in RSPE? A) Frequency chart B) Statistics table C) Percentiles table D) Cumulative frequency chart E) None of the answer choices is correct. Answer: B Difficulty: 1 Easy Topic: Bidding For a Construction Project: A Prelude to the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 45) When applying simulation to an inventory problem, which of the following would be an uncertain variable cell? A) The total profit B) The holding cost per unit C) The demand D) All of the answers choices are correct. E) None of the answer choices is correct. Answer: C Difficulty: 2 Medium Topic: Bidding For a Construction Project: A Prelude to the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

46) When applying simulation to an inventory problem, which of the following is the most appropriate choice for the results cell? A) The total profit B) The holding cost per unit C) The demand D) All of the answers choices are correct. E) None of the answer choices is correct. Answer: A Difficulty: 2 Medium Topic: Bidding For a Construction Project: A Prelude to the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 47) Which of the following are advantages of computer simulation over analytical methods like PERT/CPM for predicting the probability that a project will complete by a deadline? I. It does not need to make as many simplifying assumptions. II. It is more flexible about which probability distributions can be used. III. It provides a solution more quickly. A) I only B) II only C) III only D) I, II, and III E) I and II only Answer: E Difficulty: 2 Medium Topic: Bidding For a Construction Project: A Prelude to the Reliable Construction Co. Case Study Learning Objective: Use Analytic Solver to perform various basic computer simulations that cannot be readily performed with the standard Excel package. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

48) The sensitivity chart conveys which of the following? A) The relative frequency of various results cell values B) The increase in profit per unit increase in an uncertain variable cell C) It indicates how strongly various uncertain variable cells influence the results cell D) The mean profit E) None of the answer choices is correct. Answer: C Difficulty: 2 Medium Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Interpret the results generated by Analytic Solver when performing a computer simulation. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 49) Which of the following is not one of the charts or tables provided by RSPE? A) Frequency chart B) Statistics table C) Standard error chart D) Cumulative frequency chart E) Percentiles table Answer: C Difficulty: 2 Medium Topic: Project Management: Revisiting the Reliable Construction Co. Case Study Learning Objective: Interpret the results generated by Analytic Solver when performing a computer simulation. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 50) Which chart indicates the trend in forecast values as a particular decision variable is varied? A) Frequency chart B) Trend chart C) Cumulative frequency chart D) Statistics table E) None of the answer choices is correct. Answer: B Difficulty: 2 Medium Topic: Decision Making With Parameter Analysis Reports and Trend Charts Learning Objective: Use Analytic Solver to generate a parameter analysis report and a trend chart as an aid to decision making. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 15 Copyright © 2019 McGraw-Hill

51) Which of the following is not a characteristic of the normal distribution? A) Some value is the most likely. B) Values closest to the mean are more likely. C) It must be symmetric. D) Values cannot fall below zero. E) Extreme values are possible, but rare. Answer: D Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 52) Which of the following is not a characteristic of the triangular distribution? A) Some value is the most likely. B) Values close to the most likely value are more common. C) The most likely value is the mean. D) It can be asymmetric. E) It has a fixed upper and lower bound. Answer: C Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 53) Which of the following is not a characteristic of the lognormal distribution? A) Some value is the most likely. B) It is negatively skewed (above the mean more likely). C) Values cannot fall below zero. D) Extreme values (high end only) are possible, but rare. E) All of the answers choices are characteristic of the lognormal distribution. Answer: B Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 16 Copyright © 2019 McGraw-Hill

54) Which of the following is not a characteristic of the uniform distribution? A) It has a fixed minimum value B) It has a fixed maximum value C) Some value is the most likely D) All of the answers choices are characteristic of the uniform distribution. E) None of the answers choices is characteristic of the uniform distribution. Answer: C Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 55) Which of the following distributions is widely used to describe the time between random events? A) Uniform distribution B) Exponential distribution C) Poisson distribution D) Normal distribution E) None of the answer choices is correct. Answer: B Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

56) Which of the following distributions describes the number of times an event occurs during a given period of time or space? A) Uniform distribution B) Exponential distribution C) Poisson distribution D) Normal distribution E) None of the answer choices is correct. Answer: C Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 57) Which of the following distributions describes the number of times an event occurs in a fixed number of trials? A) Binomial distribution B) Geometric distribution C) Negative binomial distribution D) Poisson distribution E) None of the answer choices is correct. Answer: A Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

58) Which of the following distributions describes the number of trials until an event occurs? A) Binomial distribution B) Geometric distribution C) Negative binomial distribution D) Poisson distribution E) None of the answer choices is correct. Answer: B Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation 59) Which of the following distributions describes the number of trials until an event occurs n times? A) Binomial distribution B) Geometric distribution C) Negative binomial distribution D) Poisson distribution E) None of the answer choices is correct. Answer: C Difficulty: 1 Easy Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Remember AACSB: Knowledge Application Accessibility: Keyboard Navigation

60) The parameter analysis report can simultaneously vary up to how many different decision variables? A) 1 B) 2 C) 3 D) 4 E) Any number of decision variables. Answer: B Difficulty: 2 Medium Topic: Decision Making With Parameter Analysis Reports and Trend Charts Learning Objective: Use Analytic Solver to generate a parameter analysis report and a trend chart as an aid to decision making. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 61) The RSPE Solver can be used to simultaneously optimize up to how many decision variables? A) 1 B) 2 C) 3 D) 4 E) Many decision variables can be optimized simultaneously. Answer: E Difficulty: 2 Medium Topic: Optimizing With Computer Simulation Using the Solver in Analytic Solver Learning Objective: Use the Solver in Analytic Solver to search for an optimal solution for a simulation model. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

62) Which of the following distributions is positively skewed? I. Normal distribution II. Uniform distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only III and IV Answer: E Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 63) Which of the following distributions is not skewed? I. Normal distribution II. Uniform distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only I and II Answer: E Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

64) Which of the following distributions has a fixed minimum and maximum? I. Normal distribution II. Uniform distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only I and II Answer: B Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 65) Which of the following distributions has a fixed minimum and maximum? I. Normal distribution II. Triangular distribution III. Lognormal distribution IV. Exponential distribution A) I only B) II only C) III only D) IV only E) Only I and II Answer: B Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

66) Which of the following is NOT a continuous distribution? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution Answer: D Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 67) Which of the following is a discrete distribution? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution Answer: D Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 68) The relative likelihood of any particular value is given by the height of the distribution's A) central-tendency distribution. B) probability density function. C) cumulative density function. D) most likely value. E) standard deviation. Answer: B Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation 23 Copyright © 2019 McGraw-Hill

69) Which of the following is NOT a central-tendency distribution? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Uniform distribution E) Exponential distribution Answer: D Explanation: The uniform distribution does not have any unique value that is more likely than any other. Difficulty: 3 Hard Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 70) For a distribution that is positively skewed, which of the following is TRUE? A) The mean and the standard deviation are equal. B) The mean will be located to the right of the most likely value. C) The mean will be located to the left of the most likely value. D) All values are equally likely. E) The mean and the most likely value will be the same. Answer: B Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

71) Which of the following distributions would be most appropriate for modeling the number of students found in a small classroom? A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution Answer: D Explanation: Only the integer uniform distribution would allow modeling of the number of students without the possibility of fractional results. This is appropriate because students cannot be divided into fractions. Furthermore, the integer uniform distribution allows a fixed maximum and minimum value, which would reflect the fact that the number of students cannot be less than zero or more than the capacity of the classroom. Difficulty: 3 Hard Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation 72) The exponential distribution has a most likely value that is equal to A) zero. B) the mean. C) the variance. D) All of the answers choices are true. E) None of the answer choices is true. Answer: A Difficulty: 2 Medium Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Understand AACSB: Knowledge Application Accessibility: Keyboard Navigation

73) The distribution shown below is most likely which of the following?

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution Answer: D Explanation: The integer uniform distribution has discrete values. Difficulty: 3 Hard Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

74) The distribution shown below is most likely which of the following?

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Exponential distribution Answer: B Explanation: The triangular distribution has a minimum, maximum, and most likely value. Difficulty: 3 Hard Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

75) The distribution shown below is most likely which of the following?

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Uniform distribution E) Exponential distribution Answer: D Explanation: All values are equally likely in the uniform distribution. Difficulty: 3 Hard Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation

76) One way to ensure that Analytic Solver identifies an optimal solution quickly is to do which of the following? I. Set the "Max Time without Improvement" setting to zero. II. Add bounds for the decision variables. III. Add integer constraints to the model. A) I only B) II only C) III only D) Only II and III E) I, II, and III Answer: D Difficulty: 2 Medium Topic: Optimizing With Computer Simulation Using the Solver in Analytic Solver Learning Objective: Use the Solver in Analytic Solver to search for an optimal solution for a simulation model. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation

77) A manager has observed sales for a number of days and developed the following table of probabilities. Which of the following distributions would be most appropriate for modeling the daily sales? Daily Sales 100 200 300 400

Probability 0.40 0.05 0.50 0.05

A) Normal distribution B) Triangular distribution C) Lognormal distribution D) Integer uniform distribution E) Custom discrete distribution Answer: E Explanation: Only the custom distribution is capable of modeling a distribution with such widely varying probabilities. Difficulty: 3 Hard Topic: Choosing the Right Distribution Learning Objective: Describe the characteristics of many of the probability distributions that can be incorporated into a computer simulation when using Analytic Solver. Bloom's: Analyze AACSB: Analytical Thinking Accessibility: Keyboard Navigation