(30 points} A freight plane has three large compartments to carry cargo. Weight and 1.rolume limitations of these compartments are: Compartment Weight Volume (Tons) (1113) Front 10 6800 Center 16 8 700 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: Cargo Total Weight Total Volume Prot on Shipping (Tons) (m3) ($100,! ton) K1 18 8640 310 K2 15 9750 380 K3 23 13340 35!] K4 12 4680 285 Furthermore, the weight of cargoes in the respective compartments must he 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 prot. a: Describe decision variables that you use to formulate the linear programming model. You should use the following indices to simplify the description of deci- sion variables. i : indicate the type of cargo. i = 1 (K1), 2 (K2), 3 (K3), 4 (K4). j : indicate the compartment. j = 1 (Front), 2 (Center), 3 (Rear). b: Write down the objective function, by using your defined decision variables, to pursue the highest profit. c: Describe all constraints that you think should be given in the linear programming model. The format follows the requirement on Problem 1(c).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