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Billy's Bank is the only bank in a small town in Arkansas. On a typical Friday an average of 10 customers per hour arrive at the bank to transact business.

There is one single teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times can be described by the exponential distribution. Although this is the only bank in town, some people in the town have begun using the bank in a neighboring town about 20 miles away. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller at Billy's is used, find

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(a) The average time in the line.

(b) The average number in the line.

(c) The average time in the system.

(d) The average number in the system.

(e) The probability that the bank is empty

13-25

For the Billy's Bank situation, the salary and benefits for a teller would be $12 per hour. The bank is open 8 hours each day. It has been estimated that the waiting time cost per hour is $25 per hour in the line.

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(a) How many customers would enter the bank on a typical day?

(b) How much total time would the customers spend waiting in line during the entire day if one teller were used? What is the total daily waiting time cost?

(c) How much total time would the customers spend waiting in line during the entire day if two tellers were used? What is the total waiting time cost?

(d) If Billy wishes to minimize the total waiting time and personnel cost, how many tellers should be used?