A cargo transport plane is to be loaded to maximize the revenue from the load carried. The plane may carry any combination and any amount of cargoes A, B, and C. The relevant values for these cargoes are shown in the table below.
CARGO TONS REVENUE VOLUME
TYPE AVAILABLE PER TON PER TON (cu. ft.)
A 10 $700 2,000
B 12 $725 3,500
C 17 $685 3,000
The plane can carry as many as 32 tons of cargo. The plane is subdivided into compartments, and there are weight and volume limitations for each compartment. It is critical for safety reasons that the weight ratios be strictly observed. The requirements for cargo distribution are shown in the following table.
COMPARTMENT MAXIMUM COMPARTMENT
VOLUME (cu. ft.) WEIGHT/TOTAL WEIGHT RATIO
Right fore 16,000 Must equal 18% of total weight loaded
Right center 20,000 Must equal 25% of total weight loaded
Right aft 14,000 Must equal 7% of total weight loaded
Left fore 10,000 Must equal 18% of total weight loaded
Left center 20,000 Must equal 25% of total weight loaded
Left aft 12,000 Must equal 7% of total weight loaded
Which cargoes should be carried, and how should they be allocated to the various compartments? Please show formulation of model showing the decision variables, objective functions and all the individual constraints.