Q1. Farris Billiard Supply sells all types of billiard equipment, and is considering manufacturing their own brand of pool cues. Mysti Farris, the production manager, is currently investigating the production of at standard house pool cue that should be very popular. Upon analyzing the costs, Mysti determines that the materials and labor cost for each cue is $25, and the fixed cost that must be covered is $2,400 per week. With a selling price of $40 each, how many pool cues must be sold to break even? What would the total revenue be at this break-even point? (10 points) Q2. Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes that any leftover goods will have to be scrapped. How many units should be ordered in February? (20 points) "First fill the following payoff table and then use the EMV criterion to find the best option." Alternatives States of Nature Demand (units) 50 60 70 Order 50 Order 60 Order 70 Probabilities: Q3. A plant manager considers the operational cost per hour of five machine alternatives. The cost per hour is sensitive to three potential weather conditions: cold, mild, and warm. Assume that for a randomly selected day, there is a 30% probability of cold weather, 50% probability of mild weather, and 20% probability of warm weather. The following table represents the operations cost per hour for each alternative-state of nature combination: Alternatives States of Nature Weather related cost per hour Cold cost/day Mild cost/day Warm cost/day Machine 1 $50 $40 $45 Machine 2 $45 $42 $47 Machine 3 $40 $35 $54 Machine 4 $60 $25 $48 Machine 5 $45 $40 $45 Assignment 1 (Due date: October 23, 2023) MGSC 5113-18 Page 2 of 3 a) Using the optimistic and pessimistic criteria, which alternatives are best? (5 Points) b) Using the criterion of realism and equally likely criterion, which alternative are best? (5 Points) c) What alternative is best using EMV and EVPI criteria? (10 Points) d) What alternative is best using expected opportunity loss? (10 Points) Q4. Monica Britt has enjoyed sailing small boats since she was 7 years old, when her mother started sailing with her. Today, Monica is considering the possibility of starting a company to produce small sailboats for the recreational market. Unlike other mass-produced sailboats, however, these boats will be made specifically for children between the ages of 10 and 15. The boats will be of the highest quality and extremely stable, and the sail size will be reduced to prevent problems of capsizing. Her basic decision is whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With a favorable market, Monica can expect to make $90,000 from the large facility or $60,000 from the smaller facility. If the market is unfavorable, however, Monica estimates that she would lose $30,000 with a large facility and she would lose only $20,000 with the small facility. Because of the expense involved in developing the initial molds and acquiring the necessary equipment to produce fiberglass sailboats for young children, Monica has decided to conduct a pilot study to make sure that the market for the sailboats will be adequate. She estimates that the pilot study will cost her $10,000. Furthermore, the pilot study can be either favorable or unfavorable. Monica estimates that the probability of a favorable market, given a favorable pilot study, is 0.8. The probability of an unfavorable market, given an unfavorable pilot study, is estimated to be 0.9. Monica feels that there is a 0.65 chance that the pilot study will be favorable. Of course, Monica could bypass the pilot study and simply make the decision as to whether to build a large plant, small plant, or no facility at all. Without doing any testing in a pilot study, she estimates that the probability of a favorable market is 0.6. What do you recommend? Compute the EVSI. (25 points) "Use the decision tree to answer this question". Q5. Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20 percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation. There are two possible sites under consideration. One is relatively small while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is low, he will lose $10,000. Assignment 1 (Due date: October 23, 2023) MGSC 5113-18 Page 3 of 3 If he opens at Site 2 and demand is high he will generate a profit of $80,000, but he will lose $30,000 if demand is low. He also has decided that he will open at one of these sites. a) Using expected utility theory, what should Mark do under the following condition? (5 points) Note: He believes that there is a 60 percent chance that demand will be high. He assigns the following utilities to the different profits: U(50,000) = 0.72 U(-10,000) = 0.22 U(80,000) = 1 U(-30,000) = 0 b) For what value of utility for $50,000, U(50000), will Mark be indifferent between the two alternatives under following condition? (10 points) Note: He believes that there is a 50 percent chance that demand will be high. He assigns the following utilities to the different profits: U(50,000) = ? U(-10,000) = 0.22 U(80,000) = 1 U(-30,000) = 0

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