An order is placed to a firm for 25 diecast parts made from metals. Each part will be sold for $4500. The production cost for an individual part will cost $2000. At the end of an inspection, a part can be classified as good with 0.80 probability. Parts that classified as good but are not sold can be recycled at a value of $750. Parts that do not meet the inspection have a unit salvage value of $150. Firm has to pay $400 per unit short to the customer if the demand is not fully met. In addition, if the number that can be delivered is less than 23, there is an additional fixed penalty of $11,000 (i.e. if 20 parts can be delivered, the total penalty is (25-20)600 + 11,000=$14,000).

a. Find the expected profit for the given production quantity.

b. What is the production quantity that maximizes the expected profit?

c. Find the probability of losing money when the order quantity in part b. is used.

d. Assume that there is a process improvement that can improve production quality. If this improvement takes place, the probability of a given part meeting final inspection will raise to 95%. What is the maximum amount that should be paid for such an improvement?

e. Find the variance of the profit when the production quantity in part b is used.