During the early morning hours, customers arrive at a branchpost office at an average rate of 45 per hour (Poisson), whileclerks can handle transactions in an average time (exponential) of4 minutes each. (a) Find the average number of customers waitingfor service if 6 clerks are used. (b) Determine the minimum numberof clerks needed to keep the average time in the system to under 5minutes. (c) If clerk cost is $30 per hour and customer waitingtime represents a “cost” of $20 per hour, how many clerks can bejustified on a cost basis? Do not use excel. Explain every step inyour answers in detail.