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.
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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