12.23 Bill First, general manager of Worthmore Department Store, has estimated that every hour of customer time spent waiting in line for a sales clerk to become available costs the store $100 in lost sales and goodwill. Customers arrive at the checkout counter at the rate of 30 per hour, and the average service time is 3 minutes. The Poisson distribution describes the arrivals and the service times are exponentially distributed. The number of sales clerks can be 2, 3, or 4, with each one working at the same rate. Bill estimates the salary and benefits for each clerk to be $10 per hour. The store is open 10 hours per day.
(a) Find the average time in the line if 2, 3, and 4 clerks are used.
(b) What is the total time spent waiting in line each day if 2, 3, and 4 clerks are used?
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(c) Calculate the total of the daily waiting cost and the service cost if 2, 3, and 4 clerks are used. What is the minimum total daily cost?