| Compartment | Weight capacity (tons) |
Space capacity (cu ft) |
|---|---|---|
| Front | 12 | 7,000 |
| Center | 18 | 9,000 |
| Back | 10 | 5,000 |
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 airplane.
The following four cargoes have been offered for shipment on an upcoming flight as space is available:
| Cargo | Weight (tons) |
Volume (cu ft/ton) |
Profit ($/ton) |
|---|---|---|---|
| 1 | 20 | 500 | 280 |
| 2 | 16 | 700 | 360 |
| 3 | 25 | 600 | 320 |
| 4 | 13 | 400 | 250 |
Any portion of these cargoes can be accepted. The object 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.