Case 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 a average of 4 minutes. Calls tend to follow a Poisson distribution, and service 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 costumer time spend waiting for the clerk to take an order.
A) What is the average time that a 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?
Provide complete and step by step solution for the question and show calculations and use formulas.