Problem: Ashley's Department Store in Kansas City maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 12 per hour. The clerk is capable of taking an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $10 per hour, but because of lost goodwill and sales, Ashley's loses about $50 per hour of customer time spent waiting for the clerk to take an order.
Question 1: What is the average time that catalog customers must wait before their calls are transferred to the order clerk?
Question 2: What is the average number of callers waiting to place an order?
Question 3: Ashley's is considering adding a second clerk to take calls. The store would pay that person the same $10 per hour. Should it hire another clerk? Explain.