Customers call an airline call center to book seats. There are three divisions in the airline call center, one for booking first class seats, one for booking business class seats, and one for booking economy class seats. Each call center agent attends calls for both booking and cancellation. Overall, an agent in the first-class section can attend 80 calls, an agent in the business-class section can attend 100 calls, and an agent in the economy-class section can attend 120 calls per day. About 10% of the booked first class seats are cancelled later, 15% of business class seats are cancelled later, and 20% of the economy class seats are cancelled later. The calls requesting cancellation are routed to the same section where the customer booked the seats earlier. Seats cancelled will not earn any profit. Call center agents target to make at least 700 calls for first class, 1,000 calls for business class, and 2,250 calls for economy class per day. The expected profit from each booking in the first-class section is $110; business class, $95; and economy class, $55. The call center wants to determine the number of agents required to maximize its daily profit.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.
c. Compare the solution with the solution you get with the integer restrictions relaxed and indicate whether the rounded down solution is optimal.