1B) (Module 6 (Waiting Line Management)) You manage a car wash shop with one washing lane. On a typical day, the arrival rate at the shop is on average 10 cars per hour. When the cars arrive, they join the queue that feeds the washing lane. It takes on average 5 minutes to wash a car (this is the service time only in the lane). Assume that the inter-arrival times are exponentially distributed, and that the time to wash a car is also exponentially distributed.

a) What is the arrival rate and what is the service capacity of the shop (per hour)?

b) What is the average time that a customer has to wait before he is actually being served?

c) If the profits are $15 per car, how long does it take this business to generate a $180 profit.