$($Formulate a queing model$)$ The copy center at the college of business at State University has become an increasingly contentious stem among the college administrators. The department beads have complained to the associate dean about the long lines and waiting tines for their secretaries at the copy center. They Clair that it is a waste of scarce resources for the secretaries to stand in line talking when they could be doing more productive work in the office. Allegedly, Handford Burris, the associate dean, says the limited operating budget will not allow the college to purchase a new copier, or several copiers, to reliere the problem. This standoff has been going on for several years.To make her case for improved copying facilities, Lauzen Moore, the department head for management science, assigned students a dass project to gather some information about the copy center. The stadents were to record the arrivals at the center and the length of tire it took to do a cops job once the secretary actually reached a cops machine. In addition, the students were to describe how the copr center system worked.When the stadents completed the project, they tumed in a report to Professor Moore The report described the copy center as containing two machines. When secretaries arrived for a copr job, they joined a queue, which looked more like milling around to the students. But they acknowledged that the secretaries knew when it was their tura, and, in effect, ther formed a single queue for the first available copy machine Also, because cops 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 terer left the que'From the data the stadents gathered, Professor Moore is able to determine that secretaries arrive every $8$ minutes for a copr job and that the arrival rate is poison distributed Furthermore,she was able to determine that the average time it takes to complete a job is $12$ minutes and that it is exponentially distabuted.Using her own personal records and some data from the university's personnel office, Dr$.$Moore determines that a secretary$\text{'}$s average salary is $$8\mathrm{.}50$ per hout. From her academic calendar she adds up the actual days in the years when the college departmental offices are open and finds there are $247.$ Howerer, as she adds up working days, it occurs to her that in summer months, the workload is much lighter, and the copy center also probably gets less traffic. The summer includes about $70$ days, during which she expects the copy center traffic to be about half of what it is during the normal year, but she speculates that the average time of a copring job remains the sameProfessor Moore nest calls a local office supply firm to check the prices on copiers. A new copier of the type in the copy center now would cost $$36,000.$ It would also require $$8,000$ per fear for maititenance and would have a normal useful life of $6$ wearsDo row think Dr$.$ Will Moore will be able to convince the associate dean that a new copier machine will be cost$-$effective?$($show description of problem and discussion of conclusion$)$