Q$2.$ A cargo plane has three compartments for storing cargo at front, center and back. These

compartments have capacity constraints on both weight and space as given below:

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 airplane.

The following four cargoes have been offered for the shipment on the upcoming flight as space

is available:

Any portion of these cargoes can be accepted. The objective is to determine how much $($if

any$)$ of each cargo should be accepted and how to distribute each among the compartments

to maximize the total profit for the flight.

a$.$ Formulate a linear programming model for the use case

b$.$ Solve the model using simplex method, illustrate all the steps

c$.$ Demonstrate writing python code and implementing simplex method

d$.$ Discuss briefly on the inferences