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 type
Tons Available
Revenue per ton
Volume 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 Volume (cu.ft)
Compartment 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? Provide the mathematical formulation for this problem.

1076.