# Determine how much (if any) of each cargo should be accepted and how to distribute each among the compartments to maximize the total profit for the flight. Formulate the linear programming model for this problem.

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A cargo airplane operated by has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space, as summarized below:

Compartment Weight

Capacity

(tons) Space

Capacity

(cu.ft.)

Front

Center

Back 12

13

10 7,000

9,000

5,000

To ensure proper weight and balance, the weight of the cargo in the respective compartments must be the same proportion of that compartment's weight capacity.

The following four cargos have been offered for shipment on an upcoming flight as space is available:

Cargo Weight

(tons) Volume

(cu.ft./ton) Profit

($/ton)

1

2

3

4 20

16

25

13 500

700

600

400 280

360

320

250

Any portion of these cargoes can be accepted. Determine how much (if any) of each cargo should be accepted and how to distribute each among the compartments to maximize the total profit for the flight. Formulate the linear programming model for this problem.

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