Formulate this problem using goal programming and find the solution. [7. 5 marks]

A department store maintains a successful catalog sales department in which a clerk takes order by telephone. If the clerk is occupied on one, incoming phone calls to the catalog department are answered automatically by a recording machine and ask 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 12 per hours. The clerk is capable of taking an order in an average of 4 minutes. Calls tend to follow a Poisson distribution and service times tends to be exponential. The clerk is paid $10 per hour, but because of lost goodwill and sales, the company losses about $50 per hour of customer time spent waiting for the clerk to take an order.

1. What is the average time that catalog customers must wait before their calls are transferred to the order clerk?

2. What is the average no. of callers waiting to place an order?

3. The company is considering adding a second clerk to take calls. The store would pay that person the same $10 per hours. Should it hire another clerk?