A transport ship has three compartments for storing cargo: front, centre, and back. Each compartment has limits on the weight and volume of the cargo that can be carried, as summarized in the table below.
To maintain an even keel in the water, care must be taken to insure that the relative weight of cargo stored in each compartment is the same as the relative weight capacities of the compartments. For example the front compartment should carry exactly 100/(100+200+80) of the total cargo weight carried.
compartment weight limit (tons) space limit (cu. m)
front 100 500
centre 200 690
back 80 400
Three cargoes are available for shipment, as described below:
cargo weight (tons) volume (cubic m per ton) revenue ($/ton)
appliances 220 4.5 55
machine parts 150 3.7 47
lumber 300 6.0 35
You can elect to carry any portion of each cargo, and cargoes can be mixed together in the various holds. How many tons of each cargo should you carry to maximize the total revenue for the voyage?
How can I get the objective function and constraints?