THIS PROBLEM HAS TO BE SOLVED WITH CPLEX/AMPL

1 Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. a. What percentage of time is Judy idle? b. How much time, on average, does a student spend waiting in line? C. How long is the (waiting) line on average? d. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? 2 The managers of the Administrative Services Office estimate that the time a student spends waiting in line costs them (due to goodwill loss and so on) $10 per hour. To reduce the time a student spends waiting, they know that they need to improve Judy's processing time (see Problem 1). They are currently considering the following two options: a. Install a computer system, with which Judy expects to be able to complete a student request 40 percent faster (from 2 minutes per request to 1 minute and 12 seconds, for example). b. Hire another temporary clerk, who will work at the same rate as Judy. If the computer costs $99.50 to operate per day, while the temporary clerk gets paid $75 per day, is Judy right to prefer the hired help? Assume Poisson arrivals and exponential service times