A cargo plane has three compartments for storing cargo: front, center and back. These compartments have a capacity limits on both weight and space, as summarized below. Weight Capacity (Tons) 12 Compartment Front Center Back Space Capacity (cubic feet) 7000 9000 5000 18 10 Furthermore, the weight of the cargo in the respective compartments must be the same proportion of that compartment's weight capacity to maintain the balance of the airplane. The following four cargoes have been offered for the shipment on an upcoming flight as space is available. Cargo 1 Weight (tons) 20 26 2 3 Volume (cubic ft/ton) 500 700 600 400 Profit (S/ton) 320 400 360 290 35 4 13 Any portion of these cargoes 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. a. Formulate and solve a linear programming model for this mixed problem on a spreadsheet. b. Express the model in algebraic form