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Kresge's Department Store, a large retail store in Huntingdon, is also set-up to take customer orders by phone. If the clerk who services this method of ordering is occupied with a call, then other incoming calls are answered automatically by a recording machine and those customers are asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and served first. Calls come in at an average rate of 12 per hour. It takes the clerk an average of 4 minutes to take an order. Arrivals follow a Poisson distribution and service times can be described by the negative exponential distribution. The cost of the clerk is $10 per hour, but because of lost goodwill and sales, Kresge's loses $25 per hour of customer time spent waiting for the clerk to get to him/her.
a). What is the average time that catalog customers must wait before their calls are transferred to the order clerk?
b). What is the average number of customers waiting to place an order?
c). The store manager is considering adding a second clerk to take calls. The store would pay the clerk the same $10 per hour. Should the manager hire another clerk?
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