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 Front Center Back Weight Capacity (Tons) Space Capacity (Cubic Feet) 12 7,000 18 9,000 10 5,000 Furthermore, the weight of the cargo in the respective compartments must be the same proportion of the compartment's weight capacity to maintain the balance of the airplane. 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) 20 500 320 2 16 700 400 3 25 600 360 4 13 400 290 Any portion of these cargos can be accepted. The objective is to determine how much (if any) of 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 this