build the LP Model from the word problem, using your desired solution method. using ample code 5. A small cargo plane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space, as summarized in the table below. Furthermore, the weight of the cargo in the respective compartments must be the same proportion of that compartment's weight to maintain the balance of the airplane. Weight Compartment Capacity (Tons) Front 12 Center 18 Back 10 Space Capacity (Cubic Feet) 7.000 9.000 5.000 The following cargoes have been offered for shipment on an upcoming flight as space is available. Any portion of these cargoes can be accepted. Weight Volume Profit Cargo (Tons) (Cubic Feet/Ton) (S/Ton) 1 20 500 320 2 16 700 400 3 25 600 360 4 13 400 290 a). Formulate a linear programming model for this problem statement. b). What is the optimum solution for the flight? c). If Cargo #4 was unavailable, what would the new optimum mixture be