4 This problem illustrates balking. The Oryo Cookie Ice Cream Shop in Dunkirk Square has three competitors. Since people don’t like to wait in long lines for ice cream, the arrival rate to the Oryo Cookie Ice Cream Shop depends on the number of people in the shop. More specifically, while j  4 customers are present in the Oryo shop, customers arrive at a rate of (20  5j) customers per hour. If more than 4 people are in the Oryo shop, the arrival rate is zero. For each customer, revenues less raw material costs are 50¢.

Each server is paid $3 per hour. A server can serve an average of 10 customers per hour. To maximize expected profits (revenues less raw material and labor costs), how many servers should Oryo hire? Assume that interarrival and service times are exponential.