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 occu-pied on one line, incoming phone calls to the catalog department are answered automatically by a record-ing machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is trans-ferred 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 fol-low 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.
( a) What is the average time that catalog customers must wait before their calls are transferred to the order clerk? ( b) What is the average number of callers waiting to place an order? ( c) 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.