# Chapter 5S - Chapter 5S Decision Theory Problems 1 A small...

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Chapter 5S: Decision Theory Problems 1. A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm's capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Which alternative should be selected if the decision criterion is a. Maximax? b. Maximin? c. Laplace? d. Minimax regret? 2. Refer to Problem 1 . Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand: P (low) 5 .3 and P (high) 5 .7. a. Determine the expected profit of each alternative. Which alternative is best? Why? b. Analyze the problem using a decision tree. Show the expected profit of each alternative on the tree. c. Compute the expected value of perfect information. How could the contractor use this knowledge? 3. Refer to Problems 1 and 2 . Construct a graph that will enable you to perform sensitivity analysis on the problem. Over what range of P (high) would the alternative of doing nothing be best? Expand? Subcontract? 4. A firm that plans to expand its product line must decide whether to build a small or a large facility to produce the new products. If it builds a small facility and demand is low, the net present value after deducting for building costs will be \$400,000. If demand is high, the firm can either maintain the small facility or expand it. Expansion would have a net present value of \$450,000, and maintaining the small facility would have a net present value of \$50,000. p. 228 If a large facility is built and demand is high, the estimated net present value is \$800,000. If demand turns out to be low, the net present value will be −\$10,000. The probability that demand will be high is estimated to be .60, and the probability of low demand is estimated to be .40. a. Analyze using a tree diagram.

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b. Compute the EVPI. How could this information be used? c. Determine the range over which each alternative would be best in terms of the value of P (demand low). 5. Determine the course of action that has the highest expected payoff for this decision tree. 6. The lease of Theme Park, Inc., is about to expire. Management must decide whether to renew the lease for another 10 years or to relocate near the site of a proposed motel. The town planning board is currently debating the merits of granting approval to the motel. A consultant has estimated the net present value of Theme Park's two alternatives under each state of nature as shown on the following page.
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