Paul Bergey is in charge of loading cargo ships for International Cargo Company (ICC) at the port in Newport News, Virginia. Paul is preparing a loading plan for an ICC freighter destined for Ghana. An agricultural commodities dealer wants to transport the following products aboard this ship. Commodity Amount available Volume per ton Profit per ton
tons cubic feet s
1 4800 40 70
2 2500 25 50
3 1200 60 60
4 1700 55 80
Paul Bergey is in charge of loading cargo ships
Paul can elect to load any and/or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions:
Cargo hold Weight capacity tons Volume capacity(cubic feet)
Forward 3000 145000
Center 6000 180000
Rear 4000 155000
Paul Bergey is in charge of loading cargo ships
More than one type of commodity can be placed in the same cargo hold. However, because of balance considerations, the weight in the forward cargo hold must be within 10% of the weight in the rear cargo hold and the center cargo hold must be between 40% to 60% of the total weight on board.
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem and solve it using Solver.
c. What is the optimalsolution?