A foundry receives an order for four custom-designed castings. The customer will pay

$30,000 for each of four good castings. The customer will accept neither fewer nor more than four castings. It will cost $15,000 to produce each casting. Each casting is produced independently; the probability of a casting being good is estimated to be 0.90.

a. How many castings should be produced?

b. What is the probability of losing money on the transaction?

c. It has been argued that the estimate of cost to produce each casting is not very accurate.

Analyze the sensitivity of the optimum batch production quantity to errors in estimating the values of the cost parameters; determine how much the cost of producing each casting has to decrease in order to increase by one the number of castings to produce.

d. It has been argued that the estimate of the probability of a casting being good is inaccurate.

Analyze the sensitivity of the optimum batch production quantity to changes in the probability.