A Crew of Mechanics at the Highway Department Garage Repair

question 53

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 = 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). Which is cheaper, the existing system with one service crew, or a revised system with two service crews?

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Definitions:

S-Shaped

A shape that resembles the letter "S", often used to describe curves or bends in objects or structures.

J-Shaped

Describing a curve or graph that looks like the letter "J," often used to illustrate specific growth patterns or statistical trends.

Carrying Capacity

The maximum population size of a species that an environment can sustain indefinitely, given the food, habitat, water, and other necessities available in the environment.

Demographic Transition

A model describing how the birth and death rates of a population change over time as a country develops from pre-industrial to industrial economic system.