One operator services a group of ten machines. Machine run time and service durations are both exponential. Machines run for an average of 84 machines after a service, and service duration averages 28 minutes. The operator receives $19 per hour in wage and fringe benefits , and machine downtime costs $78 per hour per machine. a. If each machine produces 65 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.