Reference no: EM133217954

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 it takes the CSR an average of 3 minutes to take an order. Both inter-arrival and service times are exponentially distributed. 

The CSR is paid $20 per hour and the telephone company charges $5 per hour for the 800 line based on actual usage (assume that no additional charges are paid to the phone company for customers on hold). The company estimates that each minute a customer is kept on hold costs it $2 in customer dissatisfaction and loss of future business. 

1. What is the proportion of time that the CSR will be busy? Please express your response as a percentage 

2. What is the average time that a customer will be on hold before they get to speak with a CSR (in Minutes)? 

3. What is the average total hourly cost of operating the service, including the cost associated with waiting (in dollars)? 

4. What is the average total hourly cost of operating the service, including the cost associated with waiting, if there are 2 CSRs instead of one? Assume that a single common queue is formed for calls on hold. Also, assume that, you need two 800 lines, but pay only for actual usage (in dollars).