The supervisor at the Precision Machine Shop wants to determine the staffing policy that minimizes total operating costs. The average arrival rate at the tool crib, where tools are dispensed to the workers, is eight machinists per hour (Lamda). Each machinist's pay is $20 per hour. The supervisor can staff the crib either with a junior attendant who is paid $10 per hour and can process 10 arrivals (of machinists) per hour, or with a senior attendant who is paid $18 per hour and can process 16 arrivals per hour. Assume both the arrival rate and the service rate follow Poisson distribution.

a. Please determine the operating characteristics of Tool Crib system under either the junior attendant or the senior attendant

Operating Characteristics Junior attendant Senior attendant

Average utilization of the attendant (U) 1/10 1/16
Average No. of machinists in the system (L), i.e., idle machinists 1
Average No. of machinists in line (Lq) 1
Average time (hour) spent in the system by a machinist (W)
Average waiting time (hour) in line by a machinist (Wq)

b. Please estimate the hourly operating cost of the system under each attendant. [Hint: Operating Costs Per Hour = Lamda * W * Machinist_Wage_Rate + Attendant_Wage_Rate.] Which attendant should be selected for the Tool Crib?