Linear Programming Model.

An Airline provides weekly cargo lift to major cities in Africa. The company needs to load the four different types of cargo into freight plane and ship the loaded cargo from Cape Town to Johannesburg. Properties of these cargoes are shown on the table below. Cargo Total weight Total Volume Profit on Shipping (Tonnes) ()) ($100/ton) Q2 29 8500 Q2 17 9250 317 Q 25 14500 250 04 11 4750 297 225 The piane has three compartments to carry cargo. Weight capacities and volume limitations of these compartments are: Compartment Weight Volume (Tonnes) (3) Front 12 6500 Center 14 7625 Rear 7 4250 For saintaining the balance of the plane, the weight of cargos in the respective compartments must be the same proportion of that compartment's weight capacity It is not required to ship all of these cargos. Indeed, any proportion can be accepted. Decide how many tons of each type of cargo should be loaded on the plane to maximize the shipping profit. a) Describe decision variables that you use to model this problem. For your convenience, you can use the following indices to describe the decision variables 1: the type of cargo. 11(01), 2(Q2). 3(Q), 4(04). 3. the type of compartment. - (Front), 2(Center), 3(Rear). b) Describe 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 d) If Cargo Ki is carried on the plane, fixed cargo insurance must be paid $sex for. Update the model iven by Parts (-)-(c) to consider this insurance cost