A mechanic Bob requires on average 3 hours to complete a repair. The repair time

Question

A mechanic Bob requires on average 3 hours to complete a repair. The repair time closely follows an exponential distribution. Bob realizes that by hiring his nephew Bill as an assistant, he can reduce the average repair time to 2 hours. The repair time would still be exponential because the job structure is unchanged. For each repair job, Bob gets paid $220 if he finishes in less than 2 hours and $180 if he cannot. Assume Bob does not want to decrease his expected payment per repair job. What is the maximum amount per job that Bob would be willing to pay Bill?

Explanation / Answer

If Bob takes 3 hrs to complete a repair and if work 12 hrs a day then Bob gets paid $180 per work.
If Bob works with Bill and completes repair in 2 hrs, Bob gets $220 per work.
so the enhancement in Bob fees will be $40 per work, as Bob does not want to decrease his expected payment per repair job, Bob can offer bill the salary $40 per work.

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