A firm produces perishable food at the cost of $25 per case and in batches of 100 cases. It sells the product to a grocery chain at $30 per case. The grocery chain buys the products in lots of 100, 200, or 300 cases every morning, but does not specify its requirements to the firm in time for the production run. If the demand is less than the production, the excess produce is lost. If the demand is more than the production, the firm has agreed to satisfy the excess demand with a special production run at a cost of $35 per case. The selling price, however, is always at $30 per case. The firm has estimated that the demand is for 100 cases 20% of the days, for 200 cases 50% of the days and for 300 cases the remaining 30% of the days.
(a) Set up the payoff table for this problem.
(b) What should be the firm's production decision if the objective is to maximize expected payoff?
(c) How much discount should the firm be willing to offer the grocery chain for specifying the demand in time for each day's production run? Assume that the distribution for demand remains unchanged at 0.2, 0.5, and 0.3 for 100, 200, and 300 cases respectively.
(d) Compose a short memo for the CEO of the firm to explain why you should offer the grocery chain the per case discount determined in part (c).