Build an LP Model using AMPL from the word problem 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 Space Compartment Capacity Capacity (Tons) (Cubic Feet) Front 12 7,100 Center 18 9,100 Back 10 5.100 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) A 20 600 319 B 16 300 399 C 25 700 359 D 13 500 289 1). Formulate a linear programming model for this problem statement. 2). What is the optimum solution for the flight? 3). If Cargo number D was unavailable, what would the new optimum mixture be