The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of two 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 $3\mathrm{.}0$ hours and a

standard deviation of $2\mathrm{.}0$ hours. The company's cost of the repair operation is $$29$ per hour. In the economic analysis of the waiting line system, Robotics uses

$$38$ 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 $3\mathrm{.}0$ 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 $$33$ 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 $$4$ 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.$)$