A small business school has assigned a secretary to each of its four departments: accounting,

Question: A small business school has assigned a secretary to each of its four departments: accounting, finance, marketing, and management. Each secretary prepares class materials and correspondence only for that person’s own departmental faculty. The dean has received complaints from the faculty, however, and particularly from the accounting faculty, about delays inA small business school has assigned a secretary to each of its four departments: accounting, finance, marketing, and management. Each secretary prepares class materials and correspondence only for that person’s own departmental faculty. The dean has received complaints from the faculty, however, and particularly from the accounting faculty, about delays in getting work accomplished. The dean assigns an assistant to collect data on arrival rates and service times. After analyzing these data, the assistant reports that secretarial work arrives with a Poisson distribution at an average rate of lambda=3 request per hour for all department except accounting, which has an average rate of lambda=5 requests per hour. The average time to complete a piece of work is 10 minutes regarding of its source, and the service times are distributed exponentially. Because of budget limitations, no additional secretaries can be hired. The dean believes, however, that service could be improved if all the secretaries were pooled and instructed to receive work from the entire business school faculty. All work requests would be received at one central location and processed on a first-come, first-served basis by the first secretary who became available, regardless of that person’s departmental affiliation. Before proposing the plan to the faculty, the dean asks the assistant who collected the data to analyze the performance of the existing system and compare it with the pooling alternative. We find for the present system of independent department secretaries that accounting faculty members experience an average turn around time of ( (1) )minutes, and the faculty members in the other departments experience an average turnaround time of ( (2) ) minutes. The proposal to pool the secretarial staff improved the average turnaround time to ( (3) )minutes. Fill in the blank in (1), (2), and (3). (Hint: Use the formulas in excel)
a.(1) 60 (2) 20 (3) 11.6 b. (1) 60 (2) 30 (3) 17 c. (1) 50 (2) 10 (3) 1.6 d. (1) 20 (2) 60 (3) 11.6
For first system (Others) arrival rate lambda = 3 per hour Service rate mu =60/10=6 per hour turnaround time ( time in system, which is waiting and…View the full answer