The parts department of a large automobile dealership has a counter used exclusively for mechanics’ requests for parts. The time between requests can be modeled 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 modeled 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?
b. What is the probability that a mechanic would have to wait for service?
c. If a mechanic has to wait, how long would the average wait be?
d. What percentage of time are the clerks idle?
e. If clerks represent a cost of $ 20 per hour and mechanics a cost of $ 30 per hour, what number of clerks would be optimal in terms of minimizing total cost?