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