Radovilsky’s Department Store in Richmond Hill maintains a successful catalogue sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalogue department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of four minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The cost of the clerk is $10 per hour, but because of lost goodwill and sales, Radovilsky’s loses about $25 per hour of customer time spent waiting for the clerk to take an order.
a) What is the average time that catalogue customers must wait before their calls are transferred to the order clerk?
b) What is the average number of customers waiting to place an order?
c) Radovilsky’s is considering adding a second clerk to take calls. The store’s cost would be the same $10 per hour. Should it hire another clerk? Explain your decision.