# Question

A manufacturing company is trying to decide whether to sign a contract with the government to deliver an instrument to the government no later than eight weeks from now. Due to various uncertainties, the company isn’t sure when it will be able to deliver the instrument. Also, when the instrument is delivered, there is a chance that the government will judge it as being of inferior quality. The company estimates that the probability distribution of the time it takes to deliver the instrument is as given in the file S04_84.xlsx. Independently of this, it estimates that the probability of rejection due to inferior quality is 0.15. If the instrument is delivered at least a week ahead of time and the government judges the quality to be inferior, the company will have time to fix the problem (with certainty) and still meet the deadline. However, if the delivery is late, or if it is exactly on time but of inferior quality, the government won’t pay up. The company expects its cost of manufacturing the instrument to be $45,000. This is a sunk cost that will be incurred regardless of timing or the quality of the instrument. The company also estimates that the cost to fix an inferior instrument depends on the number of weeks left to fix it: $7,500 if there are three weeks left, $10,000 if there are two weeks left, and $15,000 if there is one week left. The government will pay $70,000 for an instrument of sufficient quality delivered on time, but it will pay nothing otherwise. Find the distribution of profit or loss to the company. Then find the mean and standard deviation of this distribution. Do you think the company should sign the contract?

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