Suppose that East-West airlines is a small airline that offers passanger air transportation between two major east coast cities, namely Boston and New York; two major west coast cities , namely San Francisco and Los Angeles; and one major midwest city, namely Chicago.East-West operates a hub in Chicago, at which passengers can change planes to their final destination. East-West Airlines owns and operates two identical Boeing 757 aircraft, each with capacity of 200 seats. The daily schedule of these airlines is shown in Table 10.1. East-west offers both discounted (Q-class) and unrestricted (Y-class) fares. Discounted tickets must be purchased fourteen days in advance of flight departure. A Q-class ticket is non-refundable, non-changeable. Unrestricted fare tickets can be purchased any time up until the departure time of the flight. A Y-class ticket is fully refundable. For the purpose of this HA, we will focus exclusively on the westbound operations. Table 10.2 shows the westbound itineraries that East-West airlines. Table 10.3 show expected demand (?) for each pair of departure-destination (disregard ?). The goal of the airline company is to choose the number of tickets for each class and eachitinerary to maximize the revenue. Each flight can carry up to 200 passengers. There are no direct flights from East Coast to West Coast, so the flights to Chicago will carry some passenger that will transfer on another plane to the West coast destination.

(a) Define decision variables

(b) Define an objective function

(c) Define constraints

(d) Find an optimal number of tickets for each combination of class and itinerary and the corresponding maximal revenue using Excel.

TABLE 10.1 The daily flight schedule for East- West Airlines. TABLE 10.2 Prices of Q-Class and Y-Class fares for the westbound itineraries of East- West Airlines. TABLE 10.3 The mean and standard deviation of the demand for travel on Mondays on westbound flights at East-West Airlines. Aircraft Number 1 1 1 1 2 2 2 2 From: BOSTON BOSTON BOSTON NEW YORK NEW YORK NEW YORK CHICAGO CHICAGO From: BOSTON BOSTON BOSTON NEW YORK NEW YORK NEW YORK CHICAGO CHICAGO City BOSTON CHICAGO SAN FRANCISCO CHICAGO NEW YORK CHICAGO LOS ANGELES CHICAGO Itinerary To: Departs: CHICAGO SAN FRANCISCO LOS ANGELES CHICAGO SAN FRANCISCO LOS ANGELES SAN FRANCISCO LOS ANGELES Itinerary To: CHICAGO SAN FRANCISCO LOS ANGELES CHICAGO SAN FRANCISCO LOS ANGELES SAN FRANCISCO LOS ANGELES Time 8:00AM EST 10:45AM CST 5:30PM PST 11:59PM CST 7:45AM EST 10:45AM CST 5:30PM PST 11:59PM CST Q-Class Fare Price $200 $320 $400 $250 $410 $450 $200 $250 25.0 55.0 65.0 24.0 65.0 40.0 21.0 25.0 City CHICAGO SAN FRANCISCO CHICAGO BOSTON CHICAGO LOS ANGELES CHICAGO NEW YORK Y-Class Fare Price $230 $420 $490 $290 $550 $550 $230 $300 Q-Class demand (Number of Passengers) T Arrives: 5.3 5.1 9.3 4.4 8.4 5.1 6.2 5.2 Y-Class demand (Number of Passengers) 20.0 40.0 Time 10:15AM CST 12:15PM PST 10:45PM CST 4:30AM EST 10:15AM CST 12:15PM PST 10:45PM CST 4:45AM EST 25.0 16.0 50.0 35.0 20.0 14.0 5.2 6.0 4.8 3.0 6.9 6.3 3.7 2.4