A freight plane has three large compartments to carry cargo. Weight and volume limitations of these compartments are: Compartment Weight (Tons) Volume (m3 ) Front 10 6800 Center 16 8700 Rear 8 5300   There are four cargos waiting to be loaded in this plane. Properties of these cargos are shown on the table below: Cargo Total Weight (Tons) Total Volume (m3 ) Profit (TL/ton) K1 18 8640 310 K2 15 9750 380 K3 13 13340 350 K4 12 4680 285   Furthermore, the weight of the cargo in the respective compartments must be the same proportion of that compartment's weight capacity to maintain the balance of the plane. Any proportion of these cargoes can be accepted. Formulate a linear programming model to maximize the profit by choosing how many tons of which cargo to load on the plane under these circumstances.

FINANCIAL ACCOUNTING
10th Edition
ISBN:9781259964947
Author:Libby
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Chapter1: Financial Statements And Business Decisions
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A freight plane has three large compartments to carry cargo. Weight and volume limitations of these compartments are:

Compartment

Weight (Tons)

Volume (m3 )

Front

10

6800

Center

16

8700

Rear

8

5300

 

There are four cargos waiting to be loaded in this plane. Properties of these cargos are shown on the table below:

Cargo

Total Weight (Tons)

Total Volume (m3 )

Profit (TL/ton)

K1

18

8640

310

K2

15

9750

380

K3

13

13340

350

K4

12

4680

285

 

Furthermore, the weight of the cargo in the respective compartments must be the same proportion of that compartment's weight capacity to maintain the balance of the plane. Any proportion of these cargoes can be accepted. Formulate a linear programming model to maximize the profit by choosing how many tons of which cargo to load on the plane under these circumstances.

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