Janson's Department Store in? Stark, Ohio, 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 who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12per hour. The clerk can take an order in an average of 3.0 minutes. Calls tend to follow a Poisson? distribution, and service times tend to be exponential.The cost of the clerk is ?$8 per? hour, but because of lost goodwill and? sales, Janson's loses about ?$30 per hour of customer time spent waiting for the clerk to take an order.
?a) The average time that catalog customers must wait before their calls are transferred to the order clerk? _____ minutes.