Jim McDonald, manager of the fast-food hamburger restaurant McBurger, realizes that providing fast service is a key to the success of the restaurant. Customers who have to wait very long are likely to go to one of the other fast-food restaurants in town next time. He estimates that each minute a customer has to wait in line before completing service costs him an average of 30 cents in lost future business. Therefore, he wants to be sure that enough cash registers always are open to keep waiting to a minimum. Each cash register is operated by a part-time employee who obtains the food ordered by each customer and collects the payment. The total cost for each such employee is $9 per hour. During lunch time, customers arrive according to a Poisson process at a mean rate of 66 per hour. The time needed to serve a customer is estimated to have an exponential distribution with a mean of 2 minutes.
1. Determine how many cash registers Jim should have open during lunch time to minimize his expected total cost per hour.
2. If Jim treats the customer as a finite calling population with the number of customers 25 and each customer arrives according to a Poisson process at a mean rate of 5 per hour. Now determine how many cash registers he should have open during lunch time to minimize his expected total cost per hour.