A firm produces a perishable food product at a cost of $10 per case. The product sells for $15 per case. For planning purposes, the company is considering possible demands of 100, 200, and 300 cases. If the demand is less than production, the excess production is discarded. If demand is more than production, the firm, in an attempt to maintain a good service image, will satisfy the excess demand with a special production run at a cost of $18 per case. The product, however, always sells at $15 per case.

a. Set up the payoff table for this problem.

b. If P(100) = .2, P(200) = .2, and P(300) 5 .6, should the company produce 100, 200, or 300 cases?