A crew for the Weston Auto repairs vehicles that break down at an average of $\backslash$lambda $=9$ vehicles per day $($approximately Poisson in nature$).$ The crew can service an average of $\backslash$mu $=14$ vehicles per day with a repair time distribution that approximates a negative exponential distribution.

$($a$)$ What is the utilization rate for this service system?

$($b$)$ What is the average time before the facility can return a breakdown to service?

$($c$)$ How much of that time is spent waiting for service?

$($d$)$ How many vehicles are likely to be in the system at any one time?

$($e$)$ How many vehicles are waiting for service

$($f$)$ If the loss of goodwill is $$20$ per hour and the Mechanic$$s salary is $$90$ per day, what is the total expected cost?