Catherine Blake, the office manager for the College of Business Administration, has received numerous complaints lately from several department chairpersons. In the past few months, the chairpersons have insisted that something be done about the amount of time their administrative assistants waste waiting in line to make copies. Currently, the college has two photocopy centers dedicated to small copying jobs: copy center A on the third floor and copy center B on the fourth floor. Both centers are self-serve and have identical processing capabilities. The copying machines are not visible to the administrative assistants from their offices. When copying is required, the administrative assistant goes to the copy room and waits in line to make the necessary copies. Catherine’s assistant, Brian, was assigned to investigate the problem.Brian reported that, on average, administrative assistants arrive at copy center A at the rate of 10 per hour and at copy center B at the rate of 14 per…

The new-accounts officer at the Bank enrolls all new customers in checking accounts. During the three-week period in August encompassing the beginning of the new school year at UTT, the bank opens many new accounts for students. The bank estimates that the arrival rate during this period will be Poisson distributed with an average of five (5) customers per hour. The service time is exponentially distributed with an average of 15 minutes per customer to set up a new account. The bank wants to determine the operating characteristics for this system to determine if the current person is sufficient to handle the increased traffic. What is the probability of no customers in the system?   What is the average number of customers waiting in the bank?   What is the average time the customer spends in the bank?   What is the average number of customers waiting in the line? What is the average time that a customer spends in the line?   Is the number of tellers sufficient to handle the increase…

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? (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?