Quantitative Methods for Business Midterm Exam
Course Introduction
Quantitative Methods for Business introduces students to the fundamental mathematical and statistical techniques used in business decision-making. The course covers topics such as data analysis, probability, forecasting, optimization, and linear programming, providing practical tools for solving real-world business problems. Through case studies and hands-on exercises, students learn to apply quantitative reasoning to areas like finance, marketing, operations, and management, enabling them to make informed, data-driven decisions in a competitive business environment.
Recommended Textbook
Practical Management Science 5th Edition by Wayne L. Winston
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Chapter 1: Introduction to Modeling
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Q1) In some applications, an analyst might present several alternative solutions from a model, and let the organization choose the best one.
A)True
B)False
Answer: True
Q2) Verification is typically the most difficult phase of the modeling process, from a mathematical perspective.
A)True
B)False
Answer: False
Q3) Which of the following is not one of the reasons for the new-found relevance of management science models?
A)Modeling is an important way to think about problems in general
B)Modeling is often now a legal requirement
C)The business world is increasingly driven by numbers
D)Modeling helps develop intuition for problems
Answer: B
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Chapter 2: Introduction to Spreadsheet Modeling
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Q1) Which of the following is a useful tool for investigating what-if questions?
A)Data tables
B)VLOOKUP function
C)Formula auditing
D)SUMPRODUCT function
Answer: A
Q2) A chart is typically much more informative to a business manager than the table of numbers it is based on.
A)True
B)False
Answer: True
Q3) The HLOOKUP function works exactly the same as the VLOOKUP function, except the lookup table is arranged in columns instead of rows.
A)True
B)False
Answer: False
Q4) A shortcut for establishing absolute references is pressing the F9 key.
A)True
B)False
Answer: False
Page 4
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Chapter 3: Introduction to Optimization Modeling
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Sample Questions
Q1) Refer to Exhibit 3-2. An advertising agency has devised a marketing plan for the Western Chassis Company that will increase the market for Deluxe chassis. The plan will increase demand by 75 Deluxe chassis per month at a cost of $100 per month. Should Western adopt the plan? Briefly explain why.
Answer: The change in the profit would be $1.8/hour shadow price times 75 hours, or $135, so Valley should adopt the plan.
Q2) [Part 5] Refer to Exhibit 3-1. Suppose the winemaker can obtain 100 addition labor hours. Can you use the sensitivity analysis obtained for Part 4 to determine her expected profit? Would her bottling plan change? Explain your answer.
Answer: Using the shadow price for labor, her profit would increase by $0.625*100=$62.5. The 100 extra hours are within the allowable increase, and would enable her to bottle considerably more (462.5 liters) desert wine, while still making 112.5 liters of table wine.
Q3) If a constraint has the equation 5x + 2y 60, then the constraint line passes through the points (0,12) and (30,0).
A)True
B)False
Answer: False
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Chapter 4: Linear Programming Models
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Sample Questions
Q1) [Part 1] Refer to Exhibit 4-3. Suppose that later in the year, venison will be out of season, but the market will be able to obtain an additional 300 pounds of pork for the same costs. Develop a processing plan in that case. How does the solution change?
Q2) Refer to Exhibit 4-1. Suppose the hospital has 40 nurses and is not allowed to hire or fire any employees, and cannot temporarily schedule nurses on their on call days. Determine a schedule that maximizes the number of weekend days off received by the nurses.
Q3) [Part 2] Refer to Exhibit 4-3. What happens to the revenue when the optimal plan changes to the one given in Part 1?
Q4) When a workforce scheduling problems is formulated as an integer programming model, it has:
A)an integer objective function
B)integer decision variables
C)integer constraints
D)all of these options
Q5) Refer to Exhibit 4-4. Assuming that all fertilizer produced can be sold, determine the optimal blending plan for the company. What is the maximum profit?
Q6) Refer to Exhibit 4-2. Determine the optimal staffing plan for the project.
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Chapter 5: Network Models
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Q1) Refer to Exhibit 5-1. Suppose the Lakeview plant was required to run at capacity. How much more would the shipping plan cost Sinclair?
Q2) For all routes with positive flows in an optimized transportation problem, the reduced cost will be:
A)zero
B)how much less shipping costs would have to be for shipments to occur along that route
C)how much more shipping costs would have to be for shipments to occur along that route
D)how much the capacity is along that shipping route
Q3) The cost of an arc in a shortest path problem is equal to the distance of the arc.
A)True
B)False
Q4) The decision variables in transportation problems are:
A)profits
B)costs
C)flows
D)capacities
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Chapter 6: Optimization Models With Integer Variables
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Q1) Refer to Exhibit 6-3. Suppose PharmaCo wants to have a backup for each city. What is the minimum number of representatives that can cover this region in that case? What are their home cities?
Q2) Solver may be unable to solve some integer programming problems, even when they have an optimal solution.
A)True
B)False
Q3) The LP relaxation of an integer programming (IP) problem is typically easy to solve and provides a bound for the IP model.
A)True
B)False
Q4) Refer to Exhibit 6-1. Which items should she take with her to her new home? What is the value of these items?
Q5) Problems with a fixed cost that is incurred only if an activity is undertaken at a positive level are inherently nonlinear.
A)True
B)False
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Chapter 7: Nonlinear Optimization Models
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Sample Questions
Q1) As an objective, minimizing the sum of squared errors is equivalent to minimizing the A)root mean square error
B)weighted sum of squared errors
C)sum of absolute errors
D)maximum absolute error
Q2) A function is concave if:
A)its slope is always nondecreasing
B)a line drawn connecting two points on the curve never lies below the curve
C)its slope is always nonincreasing
D)it is always positive
Q3) Which of the following is not one of the conditions for maximization in a nonlinear problem?
A)The objective function is concave
B)The logarithm of the objective function is concave
C)The starting values are bounded
D)The constraints are linear
Q4) Solver is guaranteed to solve certain types of nonlinear programming models.
A)True
B)False
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Chapter 8: Evolutionary Solver: An Alternative Optimization
Procedure
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Q1) If the classification matrix from a discriminant analysis shows a high percentage of correct classification, then we can be confident that the classification will work well for other populations.
A)True
B)False
Q2) In Evolutionary Solver, the initial population is chosen randomly, so the starting solution you enter in the changing cells is irrelevant.
A)True
B)False
Q3) Crossovers are rare as a genetic algorithm is generating chromosomes for the next generations.
A)True
B)False
Q4) Which of the following is not one of the Excel functions that necessitate the use of Evolutionary Solver to obtain solutions?
A)SUM
B)IF
C)MAX
D)MIN
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Chapter 9: Decision Making Under Uncertainty
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Q1) Refer to Exhibit 9-2. What should the credit union do? What is their expected profit?
Q2) Refer to Exhibit 9-2. Should the credit union purchase the report if it costs $150?
Q3) Refer to Exhibit 9-1. Suppose the farmer is not risk-neutral, but instead his behavior can be modeled using an exponential utility function with a risk tolerance parameter of 100,000. What is the most he would be willing to pay for insulation in that case?
Q4) Refer to Exhibit 9-2. The bank can thoroughly investigate the customer's credit record and obtain a favorable or unfavorable recommendation. If the credit report is perfectly reliable, what is the most the credit union should be willing to pay for the report?
Q5) Probabilities on the branches of a chance node may be ____ events that have occurred earlier in the decision tree. A)marginal due to B)conditional on C)averaged with D)increased by
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Chapter 10: Introduction to Simulation Modeling
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Q1) Refer to Exhibit 10-1. Engineering also believes the construction time will be from 5 to 9 months. However, they believe that 7 months is twice as likely as either 6 months or 8 months and that either of these latter possibilities is three times as likely as either 5 months or 9 months.
Q2) Refer to Exhibit 10-1. Company management currently has no idea what the distribution of the construction cost is. All they can state is that "we think it will be somewhere between $5,000,000 and $8,000,000."
Q3) The RAND() function in excel models which of the following probability distributions?
A)Normal(0,1)
B)Uniform(0,1)
C)Normal( 1,1)
D)Uniform( 1,1).
Q4) The three parameters required to specify a triangular distribution are the minimum, mean and maximum.
A)True
B)False
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Chapter 11: Simulation Models
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Q1) Value at risk (VAR) is an indicator of:
A)how much to bid for a project
B)the expected amount of loss for a project
C)what is nearly the worst possible outcome for a project
D)the required amount of investment required for a project
Q2) In warranty cost models, the key input random variable is product lifetime.
A)True
B)False
Q3) [Part 4] Refer to Exhibit 11-2. Are there any simulations which indicated there was a chance of getting negative NPV? Briefly explain in one sentence.
Q4) [Part 6] Refer to Exhibit 11-1. Given your answers to Parts 1 through 5, would you invest in this project?
Q5) Which of the following is typically not an application of simulation models?
A)Operations models
B)Financial models
C)Marketing models
D)Logistics models
Q6) [Part 5] Refer to Exhibit 11-1. What are the chances the firm could lose money on this project, given the price uncertainty?
Page 13
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Chapter 12: Inventory and Supply Chain Models
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Q1) Refer to Exhibit 12-3. Suppose the annual demand for the sweaters is not known with certainty, but rather is estimated to be normally distributed with mean 26,000 and standard deviation 2,000. Formulate a Solver model to find the optimal (R,Q) policy by minimizing the North Slope's expected annual cost. What is the policy, and what is the total annual cost?
Q2) Which of the following is a reason that motivates a company to carry as little inventory as possible?
A)The fixed cost of ordering
B)The desire not to run out of products that customers demand
C)The lead time to process a supply order
D)Interest costs
Q3) The only real cost benefit from synchronizing orders for several products is reduced setup costs.
A)True
B)False
Q4) In the basic economic order quantity (EOQ) model, the annual ordering cost and the annual holding cost are always equal.
A)True
B)False
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Chapter 13: Queuing Models
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Q1) The mean and standard deviation of an exponential distribution are both equal to the parameter .
A)True
B)False
Q2) Refer to Exhibit 13-3. What is the average length of the waiting line?
Q3) Server utilization is the:
A)amount of time a typical server is busy
B)fraction of time a typical server is busy
C)number of servers being used in a system
D)number of times a server is used in a system
Q4) Traffic intensity is a very useful measure of:
A)whether the system is stable or not
B)the number of customers in a system
C)the distribution of interarrival times
D)the amount of congestion in the system
Q5) In queuing systems with a finite number of customers allowed, there is no need to require that the traffic intensity be less than 1 to ensure stability.
A)True
B)False
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Chapter 14: Regression and Forecasting Models
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Q1) The percentage of variation explained R2 is the square of the correlation between the observed Y values and the fitted Y values.
A)True
B)False
Q2) Refer to Exhibit 14-1. How does the R2 value for this multiple regression model compare to that of the simple regression model estimated above? Interpret the adjusted R2 values for the two models.
Q3) The term autocorrelation refers to:
A)the analyzed data refers to itself
B)the sample is related too closely to the population
C)the data are in a loop (values repeat themselves)
D)time series variables are usually related to their own past values
Q4) The least squares line is the line that minimizes the sum of the residuals.
A)True
B)False
Q5) Refer to Exhibit 14-2. Use the information above to estimate the linear regression model.
Q6) Refer to Exhibit 14-2. Identify and interpret the percentage of variation explained (R2) for the model.
Page 16
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