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 $3\mathrm{.}1$ hours and a standard deviation of $1\mathrm{.}9$ hours. The company's cost of the repair operation is $$26$ per hour. In the economic analysis of the waiting line system, Robotics uses $$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.$)$

$=$

$\mathrm{.}2500$

Correct: Your answer is correct.

$=$

$\mathrm{.}3226$

Correct: Your answer is correct.

$($b$)$

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

Lq $=$

$1\mathrm{.}4342$

Incorrect: Your answer is incorrect.

L $=$

Wq $=$

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 $3\mathrm{.}1$ 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 $$31$ 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.$)$

Wq $=$

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 $

$.$ Based on this, the director's argument should be

$---$Select$---$

$.$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.$)$

$=1$ I

$,=$

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

$L_q=0\mathrm{.}1096,$

$L=h$

$W_q=h$

$W=$

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

$TC=$$

$w_q,|h$

$W=,|h$

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

$TC=$$

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

$.$ Based on this, the director's argument should be $---$ Select$--.$