Wendys opens a drive through with one cashier and one food preparer. Customers will first enter the "place order" line to meet the cashier and then enter the "pick up" line to get the food from the food preparer. Currently, the cashier can take an order in exactly 4 minutes and the food preparer can prepare an order in exactly 3 minutes. During an hour, 12 customers arrive on average. The inter-arrival times are exponentially distributed.
a) What is the average length of the "place order line"? What is the average length of the "pick up line"?
b) What is the average number of customers in the drive through area?
c) The manager feels that the cashier has slowed down the process and send him to a strict training class. After the class, the cashier can take an order in exactly 2 minutes. What is the capacity of the system now?
d) After the training, what is the average length of the "place order" line?