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The parts department of a large automobile dealership has a counter used exclusively for mechanics' requests for parts. The time between requests can be modelled by a negative exponential distribution that has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, and this can be modelled by a Poisson distribution that has a mean of 15. Suppose there are two clerks at the counter.
a.) On average, how many mechanics would be at the counter, including those being served? (Round your answer to 3 decimal places.)
b.) What is the probability that a mechanic would have to wait for service? (Round your answer to 3 decimal places.)
c.) If a mechanic has to wait, how long would the average wait be? (Round your answer to 3 decimal places.)
d.) What percentage of time are the clerks idle? (Round your answer to nearest whole number.)
e.) If clerks represent a cost of $29 per hour and mechanics a cost of $27 per hour, what number of clerks would be optimal in terms of minimizing total cost?
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