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 Weight capacity (tonnes) Space capacity (cubie netres) 13600 Centre Pront 20 32 16 17400 10600 Rear 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: Weight (tonnes) Volume (cubic metres/tonne) profit (/tonne) Cargo ci C2 c C4 36 30 1300 1160 620 760 700 780 Any proportion of these cargoes can be accepted. The objective is to determine how much (if any) of each cargo C1, 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. Formulate the problem as a linear program (Total 7.2) a. Explicitly define the decision variables (2.4) b. Mathematically write down the objective function (0.8) c. Mathematically write down the constraints (4.0)