A cargo plane has three compartments for storing cargo: front, centre and rear. These compartments have the following limits on both weight and space: Compartment Front Center Rear Capacity (tons) Weight (tons) Volume (m3) 10 6800 16 8700 8 5300 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 plane. The following four cargoes are available for shipment on the next flight: Cargo C1 C2 C3 C4 Weight (tons) 18 15 23 Volume (m) Profit ($/ton) 480 310 650 380 580 350 390 285 12 Any proportion of these cargoes can be accepted. The objective is to determine how much (if any) of each cargo Ci, C2, C3 and C4 should be accepted and how to distribute each among the compartments so that the total profit for the flight is maximized. (a) Formulate the above problem as a linear program (b) What assumptions are made in formulating this problem as a linear program? (C) Briefly describe the advantages of using a software package to solve the above linear program, over a judgmental approach to this