MAC Airlines is trying to decide how to partition a new plane for its Hamilton-Montreal route for the first 100 flights. The plane can seat 201 economy class passengers. A section can be partitioned off for Premium seats, however each premium seat takes the space of two economy class seats. A business class section can also be allocated, but each business class seat takes one and half economy class seats. The profit on a premium class ticket is three times the profit of an economy ticket. A business class ticket has a profit of two times an economy ticket's profit. Once the plane is partitioned into these seating classes, it cannot be changed for the first 100 flights. MAC knows, however, that the plane will

not always be full in each section. They have decided to assume that only two scenarios occur. For the first 50 of the 100 flights, they assume scenario 1 for which they can sell at most 20 premium class tickets, 50 business class tickets, and 200 economy tickets. For the remaining 50 flights, they assume scenario 2 for which these figures are 5, 10, and

150 respectively. You can assume they cannot sell more tickets than seats in each of the sections. Find a way to partition the seats to maximize the profit for the first 100 flights.

Can someone kindly help me to for this question into a Linear Programming system? (max $\displaystyle c^T x$ s.t $\displaystyle Ax >= b$)

the objective function, and the constrians.

I'm not sure how to relate the scenario 1 & 2 together to set the variables properly.

Thanks.