Sealcoat, Inc. has a contract with one of its customers to supply a unique liquid chemical product used in the manufacture of a lubricant for airplane engines. Because of the chemical process Sealcoat uses, batch sizes for the product must be 1,000 pounds. The customer has agreed to adjust manufacturing to the full-batch quantities and will order either one, two, or three batches every three months. Since production includes a one-month aging process, Sealcoat must make its production (how much to make) decision before the customer places an order. Thus the product demand alternatives are 1,000, 2,000, and 3,000 pounds, but the exact demand is unknown. Sealcoat's manufacturing costs are $150 per pound, and the product sells at the fixed contract price of $200 per pound. If the customer orders more than Sealcoat has produced, Sealcoat has agreed to absorb the added cost of filling the order by purchasing a higher-quality substitute product from another chemical firm. The substitute product, including transportation expenses, will cost Sealcoat $240 per pound. Since the product cannot be stored more than two months without spoilage, Sealcoat cannot inventory excess production until the customer's next three-month order. Therefore, if the customer's current order is less than Sealcoat has produced, the excess production will be reprocessed and will then be valued at $50 per pound. The decision in this problem is: How much should Sealcoat produce given the costs and the possible demands of 1,000, 2,000, and 3,000 pounds? From historical data and analysis of the customer's future demands, Sealcoat has developed the probability distribution for demand as follows.

Demand Probability

1,000 ............. 3

2,000 .............. 5

3,000 .............. 2

a. Develop a payoff table for the problem.

b. How many batches should Sealcoat produce every three months?