M.M. Sprout, a catalog mail-or

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 nobody hangs up in frustration over a long wait. Suppose that, on average, one call comes every 5 minutes and that it takes the CSR an average of 4 minutes to take an order. Both interarrival and activity times are exponentially distributed (i.e., they have coefficients of variation equal to 1). 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.

Estimate the following:

• The proportion of time that the CSR will be busy

• The average time that a customer will be on hold

• The average number of customers on line

• The total hourly cost of service and waiting

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