Problem 2. (18 marks in total) People's software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time required by either representative to answer a customer's questions has an exponential distribution with a mean of minutes. Calls are arriving according to a P Poisson process at a mean rate of 10 per hour. By next year, the mean arrival rate of calls is expected to decline to 5 per hour, so the plan is to reduce the number of technical representatives to one then. (a) (8 marks) Assuming that the service rate will be the same as currently next year, determine LZ, W, and W. for both the current system and next year's system. W = calls per hour L-time ratio of the minimum time taken L4-time ratio of the maximum time taken (6) (3 marke) What fraction of time is the current system empty? How about next year's system? I () (3 marks) Calculate the utilization factor of the current and next year's system. (d) (2 marks) Under the current system, what is the probability of two calls arriving per bour? (e) (2 marks) Next year, what is the probability that a customer calling in will have to wait 10 minutes or more before his/her question will be answered