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A cargo plane has three compartments for storing cargo: front, center, and back. These compartments...

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Accounting

A cargo plane 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

(Cubic Feet)

Front

12

7000

Center

18

9000

Back

10

5000

Furthermore, the weight of the cargo in the respective compartments must be the same proportion of that compartments weight capacity to maintain the balance of the airplane.

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

Cargo

Weights

(Tons)

Volume

(Cubic Feet/Ton)

Profit

($/Ton)

1

20

500

270

2

16

700

350

3

25

600

310

4

13

400

240

Any portion of these cargoes can be accepted. The objective is to 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.

Solve this model by the simplex method and determine the maximum possible profit.

Maximum profit = $

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