Operations research Quiz.

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Operations research Quiz

Problem 1 Billy’s bank is the only bank in a small town in Arkansas. On atypical 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:-

The average time in the line. The average number in the line. The average time in the system. The average number in the system. The probability that there are more than three customers in the system? The probability that the bank is empty.

Problem 2 For the Billy’s bank situation in problem , the salary and benefits for a teller would be 12$ per hour. the is open 8 hours each day. It has been estimated that the waiting time cost per hour is 25$ per hour in the line. How many customers would enter the bank on a typical day? 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? 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? If Billy wishes to minimize the total waiting time and personnel cost, how many tellers should be used?

Problem 3 In hamburger restaurant where customers from a single line for the one cashier. The average number of arrivals is 20 per hour and poisson distribution accurately defines this rate. The average service rate is 30 customer per hour , and exponential distribution defines this rate. Using kendall notation, what type of queuing system is this? What is the probability that the cashier is busy? What is the average length of the line?

How many minutes does the customer spend waiting in line as an average? How many minutes typically elapse from the time the person enters the line until the person gets the food and leaves the system? What is the probability of being more than three customers in the system? What is the total cost if the waiting cost per hour is 13$, and the service cost per hour is 15$? Suppose that another cashier is added. The restaurant would pay that person 16$ per hour .should it hire another cashier ?explain.