M.M. Sprout, a catalog mail order retailer, has one customer service Representative (CSR) to take orders at an 800 telephone number. If the CSR is busy, the next caller is put on hold. For simplicity, assume that any number of incoming calls can be put on hold and that nobody hangs up in frustration over a long wait. Suppose that, on average, one call comes in every 4 minutes and that is takes the CSR an average of 3 minuets to take an order. Both interarrival and activity times are exponentially distributed. The CSR is paid 20$ per hour, and the telephone company charges 5$ per hour for the 800 line. The company estimates that each minute a customer is kept on hold costs it 2$ in customer dissatisfaction and loss of future business.
B. More realistically, suppose that M.M. sprout has four telephone lines. At most, therefore, three callers can be kept on hold. Assume, too, that any caller who gets a busy signal because all four lines are occupied simply hangs up and calls a competitor. M.M. Sprout's average loss, in terms of current and potential future business, is $100 per frustrated caller.
Estimate the total cost of the following: -Providing Service
-Waiting
-Average hourly loss incurred because customers cannot get through