A ship has three cargo loads -forward, centre and after. The capacity limits are given:

Commodity Weight (in tonne) Volume (in cu. feet)

Forward 2000 100000
Centre 3000 135000
After 1500 30000

The following cargoes are offered. The ship owner may accept all or any part of each commodity:

Commodity Weight (in tonne) Volume (in cu. feet) Profit per tonne (in Rs)

A 6000 60 150
B 4000 50 200
C 2000 25 125


In order to preserve the trim of the ship, the weight in each load must be proportional to the capacity in tonne. The cargo is to be distributed
so as to maximize the profit. Formulate the problem as LPP model.

Please help