The parts department of the large automobile dealership has the counter employed exclusively for mechanics' requests for parts. The time between requests can be modelled by the negative exponential distribution which has a mean of 5 minutes. A clerk can handle requests at the rate of 15 per hour, and this can be modelled by the Poisson distribution which has a mean of 15. Assume there’re two clerks at counter.
a) On average, how many mechanics would be at counter, including those being served?
b) What is probability which a mechanic would’ve to wait for service?
c) If the mechanic has to wait, how long would average wait be?
d) What percentage of time are the clerks idle?
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?