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An-Ser Services is a call center operation in Wisconsin that specializes in providing answering services for financial services, insurance companies, and medical practices. The company currently uses 8 customer service representatives (CSRs) who earn a salary of $10 per hour. An-ser reports that on a typical day they received 1267 customer calls during the 6:00-10:00 am shift (assume an exponential distribution of inter-arrival times). The average processing time (the time when a CSR is helping a customer) is 90 seconds, with a standard deviation of 120 seconds. An-Ser pays $0.05 per minute for the toll-free 1-800 number, and this line charge applies to the total time that a customer is on-hold waiting to talk to a CSR, plus the time that a customer spends talking to a CSR. a. What is the CSR utilization and the average customer hold time if An-Ser uses 8 CSRs from 6:00-10:00 am? b. What is the cost of direct labor per call with 8 CSRs? (Remember: cost of direct labor = total wages per unit of time / flow rate per unit of time) c. What is the cost of line charges per call with 8 CSRs? d. An-Ser management wants to determine the optimum staffing plan for the 6:00-10:00 am shift. More CSRs will increase the cost of direct labor per call, but more CSRs will reduce the hold time for a customer and therefore reduce the line charges per call. How many CSRs should work this shift in order to minimize the total cost (direct labor + line charges)?
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