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4) A cargo plane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space as summarized below: Compartment Weight Capacity (Tons) Space Capacity (Cubic Feet) Front 12 7,000 Center 18 9,000 Back 10 5,000 The weight of the cargo in the respective compartment must be the same proportion of that compartment's weight capacity to maintain the balance of the plane. The following four cargos have been offered for shipment on an upcoming flight as space is available: Cargo Weight (Tons) Volume (Cubic Feet/Ton) Profit ($/Ton) 1 20 500 320 2 16 700 400 3 25 600 360 4 13 400 290 Any fraction of these cargos can be accepted. The objective is to determine how much (if any) each cargo should be accepted and how to distribute each among the compartments to maximize the total profit for the flight. Formulate a linear programming model for the problem. Specify the input data, decision variables, objective function, and constraints. (20 pts)

          4) A cargo plane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space as summarized below:
Compartment Weight Capacity (Tons) Space Capacity (Cubic Feet)
Front 12 7,000
Center 18 9,000
Back 10 5,000
The weight of the cargo in the respective compartment must be the same proportion of that compartment's weight capacity to maintain the balance of the plane.
The following four cargos have been offered for shipment on an upcoming flight as space is available:
Cargo Weight (Tons) Volume (Cubic Feet/Ton) Profit ($/Ton)
1 20 500 320
2 16 700 400
3 25 600 360
4 13 400 290

Any fraction of these cargos can be accepted. The objective is to determine how much (if any) each cargo should be accepted and how to distribute each among the compartments to maximize the total profit for the flight. Formulate a linear programming model for the problem. Specify the input data, decision variables, objective function, and constraints. (20 pts)

$4) A cargo plane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space as summarized below: Compartment Weight Capacity (Tons) Space Capacity (Cubic Feet) Front 12 7,000 Center 18 9,000 Back 10 5,000 The weight of the cargo in the respective compartment must be the same proportion of that compartment's weight capacity to maintain the balance of the plane. The following four cargos have been offered for shipment on an upcoming flight as space is available: Cargo Weight (Tons) Volume (Cubic Feet/Ton) Profit (/Ton) 1 20 500 320 2 16 700 400 3 25 600 360 4 13 400 290 Any fraction of these cargos can be accepted. The objective is to determine how much (if any) each cargo should be accepted and how to distribute each among the compartments to maximize the total profit for the flight. Formulate a linear programming model for the problem. Specify the input data, decision variables, objective function, and constraints. (20 pts)$

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