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 minutes 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.
Suppose that M.M. Sprout is considering adding another line in order to reduce the amount of lost business. If the installation cost is negligible, can the addition of one line be justified on economic grounds? How would it affect customer waiting time? What is the total hourly customer waiting cost? What is the average hourly loss incurred because customers cannot get through?