Linear programming problem.

A cargo plane has three compartments for storing cargo: front, center and rear. These compartments have the following limits on both weight and space"

Compartment weight capacity (tonnes) Space capacity (cubic meters)

Front 10 tonnes 6800 cubic metres

Center 16 tonnes 8700 cubic metres

Rear 8 tonnes 5300 cubic metres

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 plan

The following four cargoes are available for shipment on the next flights:

Cargo / Weight (tonnes) Volume (cubic metres/tonne) profit(pounds per tonne)

C1 , 18, 480, 310

C2 , 15, 650, 380

C3 , 23, 580, 350

C4 , 12 , 390, 285

Any proportion of these cargoes can be accepted. The objective is to determine how much (if any) of each cargo C1, C2, C3, and C4 should be accepted and how to distribute each among the compartments so that the total profit for the flight is maximized.

Define the volume constraint equations in this problem.

A -

480x11 + 650x21 + 580x31 + 390x41 <= 6800

480x12 + 650x22 + 580x32 + 390x42 <= 5300

480x13 + 650x23 + 580x33 + 390x43 <= 8700

B-

650x11 + 480x21 + 580x31 + 390x41 <= 6800

650x12 + 480x22 + 580x32 + 390x42 <= 8700

650x13 + 480x23 + 580x33 + 390x43 <= 5300

C-

480x11 + 650x21 + 580x31 + 390x41 <= 6800

480x12 + 650x22 + 580x32 + 390x42 <= 8700

480x13 + 650x23 + 580x33 + 390x43 <= 5300

D-

480x11 + 650x21 + 580x31 + 390x41 <= 5300

480x12 + 650x22 + 580x32 + 390x42 <= 8700

480x13 + 650x23 + 580x33 + 390x43 <= 6800