$!!!!$HOW TO SOLVE PART $3$ URGENT!!!!

A cargo plane has three compartments for storing goods: front, middle and rear. These compartments

have the following limits for both weight and volume:

The following four loads are available for shipment on the next flight:

Each division of these loads can be accepted. The goal is to determine how much $($if any $)$ of each cargo

can be accepted and how to distribute it on each of the compartments so that the total profit for the flight

is maximized.

Formulate this problem as an LP $.$ Give the LP standard form, the Simplex notation and the initial

Simplextableau.

Suppose the following condition: The weight of the load in the resp $.$ compartments must be

proportional to the capacity of that compartment. After all, the aircraft must be kept in balance. How

would you formulate this condition? What problem arises then? $($Think about this!$)$

The optimal solution to the problem $($from part $1)$ gives the following result:

A maximum gain of $12152$ euro $($approx$.)$ is realized by loading $10$ tons of cargo $2$ in the front, $12\mathrm{.}95$

tons of cargo $3$ and $3\mathrm{.}05$ tons of cargo $4$ in the middle, and $3$ tons of cargo $3$ and $5$ tons of $2$ cargo in

the tail.

The reduced cost and shadow prices $($different from $0)$ can be found in the following table:

A maximum gain of $12152$ euro $($approx$.)$ is realized by loading $10$ tons of cargo $2$ in the front, $12\mathrm{.}95$

tons of cargo $3$ and $3\mathrm{.}05$ tons of cargo $4$ in the middle, and $3$ tons of cargo $3$ and $5$ tons of $2$ cargo in

the tail.

The reduced cost and shadow prices $($different from $0)$ can be found in the following table:

Try to develop the optimal tableau as far as possible. Is there an alternative solution? Explain.