Write a linear program for the following problem. (Do notsolve.)
A ship is transporting rice and wheat from California to Alaska. Ithas three cargo holds with the following capacities:
• The forward cargo hold can carry at most 10,000 tons, and atmost 400,000 cubic feet
. • The middle cargo hold can carry at 5,000 tons, and at most250,000 cubic feet.
• The aft cargo hold can carry at most 12,000 tons, and at most600,000 cubic feet.
In addition, for the ship to be balanced, each cargo hold mustbe filled to the same fraction of its total capacity, with respectto tonnage.
A ton of wheat takes up 44.7 cubic feet and can be sold at aprofit of $20; a ton of rice takes up 40.9 cubic feet and can besold at a profi t of $18.
The goal is to maximize the profit from the ship’s cargo.
