A Cargo Plane Has Two Compartments for Storing Cargo-Front and Back

Essay

A cargo plane has two compartments for storing cargo-front and back. These compartments have capacity limits on both weight and space, as summarized below.

They have three available cargo for an upcoming flight. The details of the cargo are given below.

For maintaining balance, the ratio of the weight of cargo in front to the capacity of the front must be equal to the ratio of the weight of cargo at the back to the capacity of the back compartment. From each cargo, a portion of it, or the entire cargo, may be accepted. The objective is to determine how much (if any) of each of these cargo is to be accepted and how to distribute each to the front and back, so as to maximize the total profit for the flight. Formulate this as a linear program.