Find the production quantity that maximizes expected profit

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Reference no: EM132239813

A firm has received an order for 25 die cast parts made from precious metals. The parts will sell for $5000 each and it will cost $2500 to produce an individual part. The probability of a part meeting final inspection equals 0.75. Parts that meet the inspection but are not sold can be recycled at a value of $1000. Parts that do not meet the inspection have a unit salvage value of $100. A penalty clause in the contract results in the firm having to pay the customer $500 per unit short if the number of parts that can be delivered is less than 25. In addition, if the number that can be delivered is less than 23, there is an additional fixed penalty of $10,000 (i.e. if 20 parts can be delivered, the total penalty is (25-20)?500 + 10,000=$12,500).

a) Generate an Excel chart that shows the expected profit for a given production quantity.

b) Find 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. (Hint: It may be easier to find the second moment of the profit first).

Reference no: EM132239813

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