The copy centre in the Faculty of Business at Local University has become an increasingly contentious item among administrators. 

The department heads have complained to the associate dean about the long lines and waiting times for their secretaries at the copy centre. They claim that it is a waste of scarce resources for the secretaries to wait in line talking when they could be doing more productive work in the office. Mohan Nassir, the associate dean, says the limited operating budget will not allow the faculty to purchase a new copier or copiers to relieve the problem. This standoff has been going on for several years. 

To make her case for improved copying facilities, Natalja Novak, a teacher in operations management, assigned stu-dents in her class to gather some information about the copy centre as a class project. The students recorded the arrivals at the centre and the length of time it took to do a copy job once the secretary actually reached a copy machine. In addition, the students described how the copy centre system worked. 

When the students completed the project, they turned in a report to Professor Novak. The report described the copy cen-tre as containing two machines. When secretaries arrive for a copy job, they join a queue, which looked more like milling around to the students, but they acknowledged that the sec-retaries knew when it was their turn. In effect, the secretaries formed a single queue for the first available copy machine. Also, since copy jobs are assigned tasks, secretaries always stayed to do the job no matter how long the line was or how long they had to wait. They never left the queue. 

From the data the students gathered, Professor Novak was able to determine that secretaries arrived every eight minutes for a copy job and that the arrival rate was Poisson distributed. Furthermore, she was able to determine that the average time it takes to complete a job was 12 minutes, and this is exponentially distributed. 

Using her department’s personnel records and data from the university personnel office, Dr. Novak determined that a sec-retary’s average salary is $10.00 per hour. From her academic calendar, she added up the actual days in the year when the faculty and departmental offices were open and found there were 247. However, as she added up working days, it occurred to her that during the summer months the workload is much less, and the copy centre would probably get less traffic. The summer includes about 70 days, during which she expected the copy centre traffic to be about half of what it is during the normal year. She speculated that the average time of a copying job would remain about the same. 

Professor Novak next called a local office supply firm to check the prices for copiers. A new copier of the type in the copy centre now would cost $36,000. It would also require $8000 per year for maintenance and would have a normal use-ful life of six years. 

Do you think Dr. Novak will be able to convince the associate dean that a new copy machine will be cost effective?