Business Analytics
Final Exam
Course Introduction
Business Analytics is an interdisciplinary course focused on the use of data-driven techniques to inform business decision-making. Students will learn how to collect, clean, and analyze data using statistical methods and business intelligence tools. Topics include data visualization, predictive modeling, optimization, and the application of analytical approaches to a variety of business scenarios such as marketing, finance, and operations. Emphasis is placed on translating analytical findings into actionable business strategies, fostering data literacy, and developing critical thinking skills to solve complex business problems.
Recommended Textbook
Quantitative Methods for Business 12th Edition by David R. Anderson
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Chapter 1: Introduction
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Q1) A small firm builds television antennas.The investment in plan and equipment is $200,000.The variable cost per television antenna is $500.The price of the television antenna is $1000.How many television antennas would be needed for the firm to break even?
Answer: 400 television antennae
Q2) Problem definition
A)includes specific objectives and operating constraints. B)must occur prior to the quantitative analysis process. C)must involve the analyst and the user of the results.
D)each of these choices are true.
Answer: D
Q3) A toy train layout designed to represent an actual railyard is an example of an analog model.
A)True
B)False
Answer: False
Q4) The process of decision making is more limited than that of problem solving.
A)True
B)False
Answer: True
Page 3
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Chapter 2: Introduction to Probability
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Q1) It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.The test for this drug is 90% accurate.What is the probability that an athlete who tests positive is actually a user?
Answer: .2177
Q2) Two events that are mutually exclusive cannot be independent.
A)True
B)False
Answer: True
Q3) Global Airlines operates two types of jet planes: jumbo and ordinary.On jumbo jets,25% of the passengers are on business while on ordinary jets 30% of the passengers are on business.Of Global's air fleet,40% of its capacity is provided on jumbo jets.(Hint: The 25% and 30% values are conditional probabilities stated as percentages.)
a.What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
b.What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?
Answer: a..357
b..583
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Chapter 3: Probability Distributions
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Sample Questions
Q1) The Poisson probability distribution is used with a continuous random variable.
A)True
B)False
Answer: False
Q2) Customers at a popular restaurant that refuses reservations arrive according to the Poisson distribution at a rate of 4 parties every 5 minutes.What is the probability that there will be more than 2 minutes between arriving parties?
Answer: .2019
Q3) An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment.The random variable in this experiment is speed,measured in miles per hour.This random variable is a
A)discrete random variable
B)continuous random variable
C)complex random variable
D)None of these alternatives is correct.
Answer: B
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Chapter 4: Decision Analysis
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Sample Questions
Q1) Sample information with an efficiency rating of 100% is perfect information.
A)True
B)False
Q2) The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the
A)information sensitivity
B)expected value of sample information
C)expected value of perfect information
D)efficiency of sample information
Q3) For a minimization problem,the optimistic approach is often referred to as the A)minimax approach
B)maximin approach
C)maximax approach
D)minimin approach
Q4) Show how you would design a spreadsheet to calculate revised probabilities for two states of nature and two indicators.
Q5) Why perform sensitivity analysis? Of what use is sensitivity analysis where good probability estimates are difficult to obtain?
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Chapter 5: Utility and Game Theory
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Q1) The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.
A)True
B)False
Q2) A risk neutral decision maker will have a linear utility function.
A)True
B)False
Q3) When consequences are measured on a scale that reflects a decision maker's attitude toward profit,loss,and risk,payoffs are replaced by A)utility values.
B)multicriteria measures.
C)sample information.
D)opportunity loss.
Q4) With a mixed strategy,the optimal solution for each player is to randomly select among two or more of the alternative strategies.
A)True
B)False
Q5) Explain the relationship between expected utility,probability,payoff,and utility.
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Chapter 6: Times Series Analysis and Forecasting
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Sample Questions
Q1) All of the following are true about a stationary time series except A)Its statistical properties are independent of time.
B)A plot of the series will always exhibit a horizontal pattern.
C)The process generating the data has a constant mean
D)There is no variability in the time series over time.
Q2) In situations where you need to compare forecasting methods for different time periods,the most appropriate accuracy measure is
A)MSE
B)MAPE
C)MAE
D)ME
Q3) A four-period moving average forecast for period 10 would be found by averaging the values from periods 10,9,8,and 7.
A)True
B)False
Q4) If the random variability in a time series is great,a high F1F1F1S1 F1F1F10 value should be used to exponentially smooth out the fluctuations.
A)True
B)False
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Chapter 7: Introduction to Linear Programming
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Q1) The constraint 2x<sub>1</sub> F1F1F1S1 F1F1F10 x<sub>2</sub> = 0 passes through the point (200,100).
A)True
B)False
Q2) Explain the difference between profit and contribution in an objective function.Why is it important for the decision maker to know which of these the objective function coefficients represent?
Q3) The Sanders Garden Shop mixes two types of grass seed into a blend.Each type of grass has been rated (per pound)according to its shade tolerance,ability to stand up to traffic,and drought resistance,as shown in the table.Type A seed costs $1 and Type B seed costs $2.If the blend needs to score at least 300 points for shade tolerance,400 points for traffic resistance,and 750 points for drought resistance,how many pounds of each seed should be in the blend? Which targets will be exceeded? How much will the blend cost? \[\begin{array} { l | c c } & \text { Type A } & \text { Type B } \\
\hline \text { Shade Tolerance } & 1 & 1 \\
\text { Traffic Resistance } & 2 & 1 \\
\text { Drought Resistance } & 2 & 5
\end{array}\]
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Chapter 8: Linear Programming: Sensitivity Analysis and Interpretation of Solution
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Sample Questions
Q1) If the optimal value of a decision variable is zero and its reduced cost is zero,this indicates that alternative optimal solutions exist.
A)True
B)False
Q2) The reduced cost for a positive decision variable is 0.
A)True
B)False
Q3) How is sensitivity analysis used in linear programming? Given an example of what type of questions that can be answered.
Q4) The dual price associated with a constraint is the improvement in the value of the solution per unit decrease in the right-hand side of the constraint.
A)True
B)False
Q5) Relevant costs should be reflected in the objective function,but sunk costs should not.
A)True B)False
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Chapter 9: Linear Programming Applications in Marketing,
Finance, and Operations
Management
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Q1) Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.
A)True
B)False
Q2) Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.
A)True
B)False
Q3) Discuss several resource allocation problems that can be modeled by varying the workforce assignment model.
Q4) Media selection problems can maximize exposure quality and use number of customers reached as a constraint,or maximize the number of customers reached and use exposure quality as a constraint.
A)True
B)False
Q5) Explain how a matrix could be used to define the decision variables in a blending problem.
Page 11
Q6) Describe some common feature of multiperiod financial planning models.
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Chapter 10: Distribution and Network Models
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Q1) When the number of agents exceeds the number of tasks in an assignment problem,one or more dummy tasks must be introduced in the LP formulation or else the LP will not have a feasible solution.
A)True
B)False
Q2) In the general assignment problem,one agent can be assigned to several tasks.
A)True
B)False
Q3) The capacitated transportation problem includes constraints which reflect limited capacity on a route.
A)True
B)False
Q4) In the general linear programming model of the assignment problem,
A)one agent can do parts of several tasks.
B)one task can be done by several agents.
C)each agent is assigned to its own best task.
D)one agent is assigned to one and only one task.
Q5) Explain what adjustments are made to the transportation linear program when there are unacceptable routes.
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Chapter 11: Integer Linear Programming
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Q1) The LP Relaxation contains the objective function and constraints of the IP problem,but drops all integer restrictions.
A)True
B)False
Q2) Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.
A)True
B)False
Q3) Which of the following is the most useful contribution of integer programming?
A)finding whole number solutions where fractional solutions would not be appropriate
B)using 0-1 variables for modeling flexibility
C)increased ease of solution
D)provision for solution procedures for transportation and assignment problems
Q4) Most practical applications of integer linear programming involve only 0 - 1 integer variables.
A)True
B)False
Q5) Why are 0 - 1 variables sometimes called logical variables?
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Chapter 12: Advanced Optimization Applications
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Q1) Revenue management methodology can be applied in the case of nonperishable assets.
A)True
B)False
Q2) The objective for the Markowitz portfolio model is to minimize portfolio return variance.
A)True
B)False
Q3) For a typical nonlinear problem,duals price are relatively insensitive to small changes in right-hand side values.
A)True
B)False
Q4) To develop a portfolio that provides the best return possible with a minimum risk,the linear programming model will have an objective function which
A)minimizes the maximum risk.
B)minimizes total risk.
C)maximizes return and minimizes risk.
D)maximizes the minimum return.
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Chapter 13: Project Scheduling: Pertcpm
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Q1) Constraints in the LP models for crashing decisions are required to compare the activity's earliest finish time with the earliest finish time of each predecessor.
A)True
B)False
Q2) A critical activity is:
A)an activity that consumes no time but shows precedence between events
B)a milestone accomplishment within the project
C)an activity with zero slack
D)the beginning of an event
Q3) Arcs in a project network indicate
A)completion times.
B)precedence relationships.
C)activities.
D)the critical path.
Q4) Suppose that,after analyzing a PERT/CPM ntwork,the project manager finds that the project completion time is unacceptable.What are the manager's options?
Q5) Once the earliest and latest times are calculated,how is the critical path determined?
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Chapter 14: Inventory Models
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Q1) The definition of service level used in this chapter is
A)the percentage of all demand that can be satisfied from inventory.
B)the percentage of all order cycles that do not experience a stockout.
C)the percentage of demand during the lead-time period that can be satisfied from inventory
D)None of the alternatives is correct.
Q2) What could be meant by service level? Why is a clear understanding of this term important?
Q3) The time between placing orders is the lead time. A)True B)False
Q4) The terms inventory on hand and inventory position have the same meaning. A)True B)False
Q5) Annual purchase cost is included in the total cost in A)the EOQ model.
B)the economic production lot size model.
C)the quantity discount model.
D)all inventory models.
Q6) What compromise must be made in the how-much-to-order decision?
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Chapter 15: Waiting Line Models
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Q1) Queue discipline refers to the manner in which waiting units are arranged for service.
A)True
B)False
Q2) For a single-channel waiting line,the utilization factor is the probability that an arriving unit must wait for service.
A)True
B)False
Q3) The Sea View Resort uses a multiple-server queue registration system.If the average service time is 8 minutes,there are three registration clerks,and guests arrive at the rate of one every 5 minutes,find
a.F1F1F1S1 F1F1F10 and F1F1F1S1 F1F1F10.
b.the probability all three clerks are idle.
c.the probability a guest will have to wait.
d.the average time a customer is in line.
e.the average number of customers in line.
Q4) Discuss the importance of the utilization factor in a queuing system and the assumptions made about its value.
Q5) How can a system be changed to improve the service rate?
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Chapter 16: Simulation
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Q1) Simulation is an excellent technique to use when a situation is too complicated to use standard analytical procedures.
A)True
B)False
Q2) The process of determining that the computer procedure that performs the simulation calculations is logically correct is called A)implementation.
B)validation.
C)verification.
D)repetition.
Q3) A simulation model provides a convenient experimental laboratory for the real system.
A)True
B)False
Q4) Simulation is a trial-and-error approach to problem solving. A)True
B)False
Q5) How can historical information be used to create discrete probability distributions?
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Chapter 17: Markov Processes
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Q1) All entries in a row of a matrix of transition probabilities sum to 1.
A)True
B)False
Q2) A city is served by three cable TV companies: Xcellent Cable,Your Cable,and Zephyr
Cable.A survey of 1000 cable subscribers shows this breakdown of customers from the beginning to the end of August. \[\begin{array} { c | c c c }
\text { Company on } & { \text { Company on August 31 } } \\
\text { August 1 } & \text { Xcellent } & \text { Your } & \text { Zephyr } \\
\hline \text { Xcellent } & 300 & 50 & 50 \\
\text { Your } & 10 & 200 & 40 \\
\text { Zephyr } & 40 & 80 & 230 \end{array}\]
a.Construct the transition matrix.
b.What was each company's share of the market at the beginning and the end of the month?
c.If the current trend continues what will the market shares be?
Q3) Why is a computer necessary for some Markov analyses?
Q4) Explain the concept of memorylessness.
Q5) Give two examples of how Markov analysis can aid decision making.
Q6) Where is a fundamental matrix,N,used? How is N computed?
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