Find the average time in the system

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A department store in Houston maintains a successful catalog sales department in which a clerk takes orders by phone. If the clerk is occupied on one line, incoming calls are answered by recording machine, which asks to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come at rate of 14 per hour. The clerk is capable of taking an order in an average of 3 minutes. Calls tend to follow a Poisson distribution and service time is exponential. The clerk is paid $12 per hour, and cost of lost goodwill for customer waiting is $25 per hour. a- What are the arrival and service rates per hour b- Find the average time (in minutes) that a customer must wait until his/her call is transferred to the order clerk. c- Find the average number of customers waiting to place orders. d- Find the average time in the system. e- Find the utilization rate of this system. Also find the probability that there are two or more customers in the system.

Reference no: EM13962457

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