The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 2.2 hours and a standard deviation of 1.4 hours. The company's cost of the repair operation is $27 per hour. In the economic analysis of the waiting line system, Robotics uses $36 per hour cost for customers waiting during the repair process.

(a)

What are the arrival rate and service rate in jobs per hour? (Round your answers to four decimal places.)

=

=

(b)

Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.)

L_q=

L=

W_q= h

W= h

Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.)

TC = $

(c)

The company is considering purchasing a computer-based equipment repair system that would enable a constant repair time of 2.2 hours. For practical purposes, the standard deviation is 0. Because of the computer-based system, the company's cost of the new operation would be $32 per hour. What effect will the new system have on the waiting line characteristics of the repair service? (Round your answers to four decimal places. Report time in hours.)

W_q= h

W= h

Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.)

TC = $

(d)

Does paying for the computer-based system to reduce the variation in service time make economic sense? The firm's director of operations rejected the request for the new system because the hourly cost is $5 higher and the mean repair time is the same. Do you agree? How much (in dollars) will the new system save the company during a 40-hour work week? (Round your answer to the nearest cent. Enter 0 if there are no savings.)

The average savings over a 40-hour work week amount to $ .