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A Repair Shop:

Another Dynamic Simulation Model

The Gotham Taxi Company has a fleet of 500 taxicabs. On any
given day of use, a taxi has an 0.4% chance of breaking down, independent of all
other taxis. Broken-down
taxis are towed overnight to the company repair shop. They return
to service the day after they are fixed. Each day a taxi spends in
the shop costs the company $350 in lost profits.

There are three mechanics Gotham is considering hiring to work in the
repair shop: Larry, Moe and Curly. Each can fix one to three
taxis per day.

Larry would cost the company $300 per day. On any given day, there
is 20% probability he can only fix one taxi, and a 40% probability he will
be able to fix either two or three.

Moe costs $250 per day. He has an equal probability of being able
to fix either one, two, or three taxis on any given day.

Curly costs $200 per day. On any given day, there is a 50% chance
he can fix only one cab, a 30% chance he will be able fix two, and a 20%
chance that he will be able to fix three.

The company may hire any combination of the three mechanics: any one,
any two, or all three. Explain why you can tell, prior to performing
any simulation, that the option of hiring just Curly will not be workable.
Simulate each possibility by 1000 trials of 100 days each. Which possibility
gives them the lowest average cost? What is the average number of taxis in
the shop when you adopt this policy?