A small suburban post office is frequented by customers at the rate of 6 per hour. The post office has a single employee who typically processes each customer's request at an average rate of 5 minutes per transaction.
a) What is the utilization rate of this service system?
b) What is the average number of customers in line?
c) What is the average time that each customer spends waiting in line (in minutes)?
d) What is the average time that each customer spends from the time they get on line until after they have received the service (in minutes)?
e) The postmaster has been receiving complaints from customers about long waiting times. The postmaster is considering hiring an additional employee who will also be able to process each customer's request at the same rate of 5 minutes per transaction. Assume that the post office pays its employees $30 per hour and that the cost of customer waiting time while in line, in terms of customer dissatisfaction and goodwill, is $8 per hour. Should the postmaster hire an additional employee? Provide all relevant cost calculations and explain your answer.}