Speedy copy center located on Capitol Hill in Washington DC

Speedy copy center located on Capitol Hill in Washington D.C. has three coin operated copying machines used primarily by U.S. Senators to make copies of their confidential diaries and illegal agreements with foreign governments and corporations. The owner, Hugh Makeham, is a former Xerox repairman and can fix a broken machine within 20 minutes on the average. Many times the machines are only jammed and he can get them working again quickly so the exponential will describe his repair time distribution. The time-to-breakdown of a freshly repaired copier averages 60 minutes and is also exponentially distributed.

His revenue when all machines are working averages $80/hr per machine. When one machine is broken his revenue drops to $60/hr per working machine because of balking. When two machines are broken his revenue from the remaining machine decreases to $50/hr. When all machines are broken his revenue naturally drops to zero.

A.Compute his average hourly revenue.

B. If he employs a second, equally competent, repairman, what will be his total expected hourly income?

C. what is the largest hourly wage he can pay the employee without decreasing the expected hourly rate he earned when working alone?

Please show steps and equations, trying to learn how to do this one.

Solution

First we assume that all the three machines are freshly repaired, and it is also assumed that the machines function/fail independent of each other.

Here, average time to fail is 60 minutes while hte income for each hour is $80 if all three work, $60 if two of them are working, and $50 if only one is working.

A. Probability of no machine failing is 0.0498, one machine failing is 0.6321, while two machines failing is 0.3996, and for three machines failing is 0.2526. Hence, the average revenue is 0.0498*80 + 0.6321*60+0.3996*50 = 61.89.

B.