2 Suppose a supermarket uses a system in which all customers wait in a single line for the first available cashier.

Assume that the service time for a customer who purchases k items is exponentially distributed, with mean k seconds.

Also, a customer who purchases k items feels that the cost of waiting in line for 1 minute is $

k 1 . If customers can be assigned priorities, what priority assignment will minimize the expected waiting cost incurred by the supermarket’s customers? Why would a customer’s waiting cost per minute be a decreasing function of k?