A Crew of Mechanics at the Highway Department Garage Repair

question 45

Essay

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 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 probability that the system is empty?
b.What is the probability that there is precisely one vehicle in the system?
c.What is the probability that there is more than one vehicle in the system?
d.What is the probability of 5 or more vehicles in the system?

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Definitions:

Pure Rent

Pure Rent refers to the income earned from the use of land or other natural resources when supply is perfectly inelastic.

Fixed Supply

A situation where the quantity of a good available is constant and does not change in response to price changes.

One-Of-A-Kind

Unique, without any identical counterpart.

Pure Rent

Payment to a factor of production (land, specifically) in excess of what is needed to keep it in its current use.