US Steel Tubular Products (USTP) Inc. is in the process of hiring a repair person for a 3-machine processing department. Two candidates are being considered. The first candidate can perform

repairs at the rate of 3 machines per hour and earns $25 an hour. The second candidate, being more skillful, receives $35 an hour and can repair 4machines per hour. USTP estimates that each broken machine will incur $60 per hour due to lost production.Assuming that machine breakdowns occur according to a Poisson distribution with a mean of 2 per hour (per working machine) and that the repair time is exponential, which repair person should be hired? (a) (2 points) Define the states, classify the queueing system, draw the state transition rate diagram with the transition rates, given that 2 is the breakdown rate per working machine and µ is the repair rate for the repair person. (b) (3 points) Find the steadystate probabilities for each repair person (unskillful and skillful). (c) (2 points) Determine the average number of broken machines for each case (unskillful repair person and skillful repair person). nts) Determine the average cost per hour for each case and decide which repair person should be hired.