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) =.3 and P(high) =.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? 5. Determine the course of action that has the highest expected payoff for this decision tree. 9. A firm must decide whether to construct a small, medium, or large stamping plant. A consultant's report indicates a .20 probability that demand will be low and an .80 probability that demand will be high. If the firm builds a small facility and demand turns out to be low, the net present value will be $42 million. If demand turns out to be high, the firm can either subcontract and realize the net present value of $42 million or expand greatly for a net present value of $48 million. The firm could build a medium-size facility as a hedge: If demand turns out to be low, its net present value is estimated at $22 million; if demand turns out to be high, the firm could do nothing and realize a net present value of $46 million, or it could expand and realize a net present value of $50 million. If the firm builds a large facility and demand is low, the net present value will be $20 million, whereas high demand will result in a net present value of $72 million. a. Analyze this problem using a decision tree. b. What is the maximin alternative? c. Compute the EVPI and interpret it. d. Perform sensitivity analysis on P(high)