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?