21 A local office of the Department of Motor Vehicles

(DMV) wishes to overcome the reputation of making citizens wait in line for extremely long times before being able to conduct their business. Accordingly, the DMV is analyzing how best to serve the driving public. Its goal is to make sure that citizens will not have to wait more than five minutes before they are engaged in service with a clerk. The DMV currently has eight clerks to serve people. If a clerk is not busy with customers, he can fill his time with filing or processing mailed-in requests for service.
On a typical day, drivers come into the DMV according to the following pattern:
TIME ARRIVAL RATE (customers/hour)
8 a.m .–10 a.m . 20 10 a.m .–2 p.m . 40 2 p.m .–5 p.m . 25 Arrivals follow a Poisson distribution. Service times follow an exponential distribution, with an average of 10 minutes per customer. How many clerks should be on duty during each period to maintain the desired level of service? You may use Excel’s Goal Seek procedure to find the answer.