2 (30 points) A freight plane has three large compartments to carry cargo. Weight and volume limitations of these compartments are: Compartment Weight Volume (Tons) (m) Front 10 6800 Center 16 8700 Rear 8 5300 There are four types of cargo waiting to be loaded in this plane and shipped from Detroit to Los Angeles. Properties of these cargoes are shown on the table below: K1 Cargo Total Weight Total Volume Profit on Shipping (Tons) (m) ($100/ton) 18 8640 310 K2 15 9750 380 K3 23 13340 350 K4 12 4680 285 Furthermore, the weight of cargoes in the respective compartments must be the same proportion of that compartment's weight capacity to maintain the balance of the plane. Any proportion of these cargoes can be accepted. Decide how many tons of each type of cargo should be loaded on the plane to maximize the shipping profit. d: If Cargo K1 is carried on the plane, a fixed cargo insurance must be paid $50,000 for. Update the model given by Parts (a) - (c) to consider this insurance cost