2. A cake ordering shop has two lines, one for service A and the other for service B. Each line has its own cake ordering machine. For each queue, customers arrive by Poisson process with an average rate of 3 customers per hour, and there is a representative taking the orders. The service time for each representative follows exponential distribution with a mean of 15 minutes.

I. How long is a wait to be served in each line, on average?

II. How many customers are served by this cake ordering shop, on average?

Assume there have been changes. The representatives are trained such that each of them can deal with both service A and service B, with a fixed time of 15 minutes. The two lines are combined into one with one shared machine.

(c) How will the average wait time change? Why

(d) How will the average utilization of the representatives change?