One operator services a group of five machines. Machine run time and service durations are both Exponential. Machines run for an average of 90 minutes after a service, and service duration averages 35 minutes. The operator receives $20 per horn- in wage and fringe benefits, and machine downtime costs $70 per hour per machine.
a. If each machine produces 60 piece s per hour while running, find the average hour Iv output of each machine when waiting and service times are taken into account.
b. Determine the optimum number of operators.