# solution

For the Billyâ€™s Bank situation in Problems 12-24 and 12-25, 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.

(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?

Problem 12-24

Billyâ€™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. If a single teller at Billyâ€™s is used, find

(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

Problem 12-25

Refer to the Billyâ€™s Bank situation in Problem 12-24. Billy is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers, and he assumes that this will cut the waiting time in half. 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 second teller is added, find

(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.

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