Paul Bergey is in charge of loading cargo ships

Paul Bergey is in charge of loading cargo ships in International Cargo Company (ICC) at the port of Newport News, Virginia. Paul is preparing a loading plan for an ICC freighter destined for Ghana. And agricultural commodities dealer would like to transport the following products aboard this ship.
Commodity Amount Available(Tons) Volume per Ton(Cubic feet) Profit per Ton($)
1 4,800 40 70
2 2,500 25 50
3 1,200 60 60
4 1,700 55 80
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 3,000 145,000
Center 6,000 180,000
Rear 4,000 155,000
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% and 60% of the total weight on board.
a. Formulate an ILP model for this problem.
b. Implement your model in Excel and solve it.
c. What is the optimal solution?