During the Early Morning Hours, Customers Arrive at a Branch

Essay

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each.Find:
(A) the average number of customers waiting for service if 6 clerks are used
(B) the minimum number of clerks needed to keep the average time in the system to under 5 minutes
(C) If clerk cost is $30 per hour and customer waiting time represents a "cost" of $20 per hour, how many clerks can be justified on a cost basis?