Customers arrive at Mike & Steve’s bookstore according to a Poisson process at a mean rate of 48 per hour. The store pays its sales clerks $7.50 per hour in wages and benefits. Mike and Steve’s estimates the goodwill cost of a customer waiting to be served at $6.00 per hour and the goodwill cost of a customer being served at only $1.00 per hour. Customer service time follow an exponential distribution and average 2 minutes. Required:
a. Determine the number of sales clerks Mike & Steve’s should employ to minimize the store’s total average hourly costs.
b. If the customer arrival rate increases by 50% and the goodwill cost of a customer waiting to be served and being served were doubled, determine how many sales clerks Mike & Steve’s should employ to minimize the store’s total average hourly costs?