You are the manager of a tech support center for a technology company. Your call center is currently split into two departments – billing/purchasing and complaints, each with its own dedicated telephone number. Based on historical estimates, you know that customers call at an average rate of 1 every minute on each phone number. In each department, you have 2 service representatives that take an average of 1.5 minutes to handle each call, and you rent 7 telephone lines for each number. You plan to merge the two departments and cross-train all the workers so they can handle all calls. No new capacity is added, i.e., the call center will still have 14 telephone lines and 4 service representatives, but only 1 phone number. All inter-arrival and service times are exponentially distributed.

a) Does the proportion of callers getting a busy signal increase, decrease, or remain unchanged?

b) Does the average flow time of the customers increase, decrease, or remain unchanged?

Please show work.