# Integer Programming Problem: Package Express Carrier

A package express carrier is considering expanding the fleet of aircraft used to transport packages. There is a total of $220 million allocated for purchases. Two types of aircraft may be purchased - the C1A and the C1B. The C1A costs $25 million, while the C1B costs $18 million. The C1A can carry 60,000 pounds of packages, while the C1B can only carry 40,000 pounds of packages. The company needs at least eight new aircraft. In addition, the firm wishes to purchase at least twice as many C1Bs as C1As. Formulate this as an integer programming problem to maximize the number of pounds that may be carried.

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#### Solution Preview

This is an integer programming model.

Let the number of C1A aircrafts to be purchased is x and that of C1B be y.

Objective:

We are required to maximize the total number of pounds to be carried.

Maximize 60000x + 40000y subject to the following constraints:

Constraints:

x + y ? 8

y ? 2x

25000000x + 18000000y ? 220000000

x, y: ...