A small building contractor has recently experienced two successive years in which work opportunities exceeded the firms capacity. The contractor must now make a decision on capacity for next year. Estimated profit for each alternative under each of the two possible states of nature for next years demand is shown to the right.

Suppose that, after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand as: P(low) = 0.3 and P(high) = 0.7.

a) Determine the expected profit of each alternative. Which alternative is best?

b) Analyze the problem using a decision tree. Show the expected profit of each alternative on the tree.

c) Calculate the expected value of perfect information. How could the contractor use this knowledge?

d) Construct a graph that will enable you to perform sensitivity to a probability on the problem. Over what range of P(high) would each of the alternatives be best?

Alternatives Do nothing Expand Subcontract Next year's Demand Low High $50* $60 20 80 40 70 *profit in $ thousands