A Crew of Mechanics at the Highway Department Garage Repair

Essay

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 12 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?