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CWD Business systems maintains a successful Telecom sales department for Top up call credit in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the department are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 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 times tend to be exponential. The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 per hour of customer time spent waiting for the clerk to take an order. Part A Answer the following questions:
a. What is the probability that no customers are in the system (Po)?
b. What is the average number of customers waiting for service ( Lq)?
c. What is the average number of customers in the system (L)?
d. What is the average time a customer waits for service(Wq)?
please explain and show workings
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