A Crew of Mechanics at the Highway Department Garage Repair

question 47

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 = 10 vehicles per day with a repair time distribution that approximates an 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?

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Definitions:

Income Statement

A financial report that shows a company's revenue, expenses, and profits over a specific period.

Present Value

The current value of a future sum of money or stream of cash flows given a specified rate of return, crucial in discounting and investment decision making.

Compounded Annually

A method of calculating interest where the accumulated interest is added to the principal at the end of each year, thereby earning interest in subsequent years.

Present Value

The calculated worth today of a future monetary sum or repetitive cash flows, utilizing a predetermined return rate.