Linear programming

Sean Skippers is in charge of load planning for cargo ships for Chase Shipping Inc. (CSI).  Sean is preparing a load plan for a CSI freighter destined for China.  An agricultural commodities dealer would like to transport three commodity products aboard this ship.  The shipping characteristics of these commodities are shown below.

Amount                 Volume per Ton          Profit per Ton

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Commodity           Available (tons)           (cubic feet)                        ($)

1                         4800                            40                                70

2                         2500                            25                                50

3                         2900                            60                                80

Sean 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                                        145,000

Center                            6000                                        180,000

Rear                                4000                                        155,000

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.  Structure as a linear programming problem (decision variables, objective function, and constraints).  You do not need to solve this problem, just structure it.

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