A small airline, Ivy Air, flies between three cities: Ithaca, Newark, and Boston. They offer several flights but, for this problem, let us focus on the Friday afternoon flight that departs from Ithaca, stops in Newark, and continues to Boston. There are three types of passengers:
(A) Those traveling from Ithaca to Newark
(B) Those traveling from Newark to Boston.
(C) Those traveling from Ithaca to Boston
The aircraft is a small commuter plane that seats 30 passengers. The airline offers three fare classes:
(a) Y class: full coach
(b) B class: nonrefundable.
(c) M class: nonrefundable, 3-week advanced purchase
Ticket prices, which are largely determined by external influences (i. e., com petitors), have been set and advertised as follows:
Ithaca-Newark Newark-Boston Ithaca-Boston
300 160 360
220 130 280
100 80 140
Based on past experience, demand forecasters at Ivy Air have determined the following upper bounds on the number of potential customers in each of the 9 possible origin-destination/fare-class combinations:
Ithaca-Newark Newark-Boston Ithaca-Boston
4 8 3
8 13 10
22 20 18
The goal is to decide how many tickets from each of the 9 origin/destination/fare- class combinations to sell. The constraints are that the plane cannot be overbooked on either of the two legs of the flight and that the number of tickets made available cannot exceed the forecasted maximum demand, The obiective is to maximize the revenue. Formulate this problem as a linear programming problem