Question

A hamburger shop has three competitors. Since people do not like to wait in long lines for hamburger, the arrival rate to the shop depends on the number of people in the shop. While n <= 4 customers are present in the shop, customers arrive at a rate of (20-5n) customers per hour. If more than 4 people are in the shop, the arrival rate is zero.

For each customer, revenues less raw material costs are 50 cent. 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 the shop hire? Assume that interarrival and service times are exponential.

Answer 1