(11 marks) A local university has a tech support centre for students, with 3 support staff working at a time. Requests for support during the week average 9 per hour and tend to be Poisson. Support time averages 16 minutes per request and follows an exponential distribution. Calculate the following performance measures (6 marks): a) Support staff utilization: b) The average number of students waiting: c) The average time in minutes) students wait for a support staff: d) The probability all support staff will be busy when a request comes in: | The tech support centre is trying to determine if they need additional support staff. To assist their decision making, answer the following (5 marks): e) If they added one more support staff, what would be the average wait time in minutes)? f) If the support centre has a desired wait time of no more than 45 seconds, how many staff should they have working? (HINT: be sure the desired wait time is in the same time unit as your arrival and service rates)