Final Exam 531 Fall 2023

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George Mason University *

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531

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Finance

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Jan 9, 2024

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4

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Fall 2023 OR 531-DL4 Final Exam INSTRUCTIONS 1. Description You will have 8 hours to complete the four problems plus a bonus question for the exam. The final will open on Monday Dec 11 at 4:00 pm as an assignment on blackboard. 2. Due Date (All times in ET) This Test is due on Dec 11, 2023 at 11:59 PM EDT. 3. This is an open book test and is an individual assignment. 4. Please save your work in two excel files (keep your simulation problem in a separate excel file) and save as lastname.firstname-optimization.xls and the simulation file as lastname.firstname-sim.xls. 5. Save your work and answers in an Excel file, so I can see how you have formulated the problems using the frontline solver software 6. Please also email your excel files to me at jfergus3@gmu.edu Problem #1 (Chapter 12) (25 points) A painting operation is scheduled in blocks, where each block involves painting products with a particular color. Cleaning time is required in between each pair of blocks so that the equipment can be prepared for the new color. In each cycle there is one block of each color, and the total painting time is determined by the volume of orders. However, the actual schedule length is determined by the sequence in which the blocks are scheduled, since the cleaning time depends on the color in the previous block and the color in the next block. The following table gives the number of minutes required to clean the equipment, according to the color pair. Using your Frontline solver software solve the optimization problem to answer the questions below: a) What block sequence minimizes the amount of time spent in cleaning during a full cycle? b) What is the minimum number of minutes devoted to cleaning? c) What would be the minimum block sequence and time devoted to cleaning if you are told that color 4 cannot follow color 1 in the sequence and color 6 cannot follow color 5 in the sequence? Problem #2 (Chapter 13) (25 points) One of our corporate competitors is threatening us with a lawsuit for patent infringement. The competitor is already in court in a similar lawsuit against another firm, and our legal staff estimates that there is a 40 percent chance that our competitor will prevail. One option open to us is to settle out of court now; the alternative is to wait until the current case is resolved before taking action. If our To Color From Color 1 2 3 4 5 6 1 - 4 8 6 8 2 2 5 - 7 11 13 4 3 11 6 - 8 4 3 4 5 7 2 - 2 5 5 10 9 7 5 - 2 6 8 4 3 6 5 -
competitor loses the other suit, it will not pursue an action against us. On the other hand, if the competitor wins, it is likely to sue us. Our legal staff estimates that likelihood at 70 percent. They further estimate that the suit would be brought for $20 million. We can settle now for $5 million. If the competitor sues us, we can negotiate a settlement, go to trial and contest the patent infringement claim, or go to trial and concede the patent infringement but fight the settlement amount. In either case, of course, the trial will dictate the monetary outcome. Our legal staff estimates that a negotiated settlement would cost us roughly $15 million. If we contest the patent, we have a 30 percent chance of winning the suit. If we concede the patent and contest the settlement amount, then the only question would be the size of that amount. Our legal staff envisions two possibilities: High, at $25 million, with a 60 percent probability, and Low, at $5 million, with a 40 percent probability. Using your Frontline solver software solve the decision analysis problem to answer the questions below: a) What is the best decision based on the expected payoff criterion? b) What is the expected payoff? c) Using the psisenvalue and psisenparameter functions, create a sensitivity analysis to show how the best decision and expected payoff would change if the probability of the opponent winning is varied from .1 to .9 by .1 increments. Problem #3 (25 points) show answers in a separate tab in your excel spreadsheet a) Binary and logical relationships. Which of the following constraints represents at most one project can be selected? y4 = y5 = 1, y2 + y5 > 1, y4 + y5 < 1, or y4 + y5 = 1 b) Binary and logical relationships. Which of the following constraints prohibits the combination? y4 = y5 = 1, y2 + y5 > 1, y4 + y5 < 1, or y4 + y5 = 1 c) Which of the following is a uniform distribution? #1 #2 #3 d) Based on the figure below, what is the probability that your model’s value will be >= $0?
Problem #4 (Chapter 14) (25 points) Butson Stores faces a problem in maintaining sufficient cash balances for operations over the first six months of the year. Each month, they must pay certain fixed costs and taxes (see the following table), as well as materials costs that run about 80 percent of the current month’s sales. Monthly cash receipts consist of revenues from the previous month’s sales, as well as 1 percent interest on short-term cash balances. The company enters the six-month period with a cash balance of $250,000 and wishes to maintain at least that balance each month in order to cover cash needs. December sales of $1.4 million have just been recorded. If Butson finishes a month with less than $250,000 in cash, the company can take out a one-month loan at 2 percent interest. The principal and interest are repaid in the following month. Butson’s marketing department has made estimates (in thousands) for the mean and standard deviation of sales in each of the next six months (see the following table). Fixed Costs and Taxes (000) Mean Sales (000) Standard Deviation of Sales (000) January 250 1800 80 February 350 1500 80 March 300 2000 90 April 400 1700 90 May 350 2200 100 June 350 1900 100 Using your Frontline solver software solve the simulation problem to answer the questions below: a) How large their maximum monthly loan is likely to be, and how likely they are to exceed their current credit limit of $750,000? b) How much on average they will have to pay in interest costs for loans? c) Fit the following table to a distribution and use this distribution for January – June actual sales (000). 1847 1841 1695 1969 1926 1901 1790 1824 1823 1853 1704 1814 2005 1893 1802 2034 1817 1885 1742 1934 1826 1874 1856 2030 2028 1906 2027 1875 1859 1755 1787 1861 1916 1696 1959 1862 1645 1889 1736 1968
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