5. A semiconductor facility has received an order for 4 wafers. The customer pay

Question

5. A semiconductor facility has received an order for 4 wafers. The customer pays 20000 TL for this order (this is the price for the complete order of 4 wafers) but insists on exactly 4 wafers and does not accept deliveries for other quantities. The production cost per wafer is 1000 TL and unused wafers do not have any value. Wafer production is subject to errors and the historical probability that a wafer of this type is satisfactory is 0.8. a. What is the expected profit if exactly 4 wafers are scheduled for production? b. What is the probability of losing money when exactly 4 wafers are produced? c. What is the expected profit if 6 wafers are scheduled for production? d. The facility would like to contract with an insurance company to cover some of the production risks. The insurance company proposes a contract that reimburses the production costs of up two wafers (i.e for each wafer that is unsatisfactory the insurances reimburses the facility 1000 TL) What is the maximum payment that the facility would make for such a contract if 6 wafers are scheduled for production?

Explanation / Answer

A)

The selling price for the 4 wafer is 20000 T and production cost is 4000 T. Hence the expected profit is 20000 - 4000 = 16000T.

B)

The probability of success is 0.8. Thus probability of losing money = 1-0.8 = 0.2

C)

If 6 wafers are under production, customer will only pay for the 4 wafers.

So profit = selling price - cost = 20000T - 6000T = 14000T

D)

Though there are 6 wafers under production but insurance company has agreed to pay for only 2 wafers cost reimbursement to the company. Hence total cost for 2 wafers i.e 2000T will be reimbursed maximum by insurance company.

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