One operator services a bank of five machines. Machine running time and service time are both exponential. Machines run for an average of 90 minutes between service requirements, and service time averages 35 minutes. The operator receives $ 20 per hour in salary and fringe benefits, and machine downtime costs $ 70 per hour per machine.
a. If each machine produces 60 pieces per hour while running, find the average hourly output of each machine, when waiting and service times are taken into account.
b. Determine the optimum number of operators.