*4. A machine shop includes 20 machines and 3 repairpersons. A working machine breaks down randomly according to a Poisson distribution. The repair time per machine is exponential with a mean of 6 minutes. A queuing analysis of the situation shows an average of 57.8 calls for repair per 8-hour day for the entire shop. Suppose that the production rate per machine is 25 units per hour and that each produced unit generates

$2 in revenue. Further, assume that a repairperson is paid at the rate of $20 an hour.

Compare the cost of hiring the repairpersons against the cost of lost revenue when machines are broken.