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 would like to transport the following products aboard this ship.

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:

Only one type of commodity can be placed into any 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 ILP model for this problem.
b. Create a spreadsheet model for this problem and solve it using Solver.
c. What is the optimalsolution?

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Amount Available (tons) 4,800 2,500 1,200 1,700 Volume per TonProfit per Ton Commodity (cubic feet) 40 50 5 Cargo Hold Weight Capacity (tons Volume Capacity(cubic feet) Forward Center Rear 3,000 6,000 4,000 145,000 180,000 155,000