A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.
-The utilization is:
A) .30
B) .45
C) .57
D) .85

Question

Quizplus · Accepted Answer

Utilization = Arrival rate (λ) * Service time (1/μ)
λ = 4 breakdowns per day
μ = 7 repairs per day
Service time = 1/μ = 1/7 day per vehicle
Utilization = 4 * (1/7) = 0.57 or 57%
Therefore, the best choice is C.

A Crew of Mechanics at the Department of Transportation Garage