# Simplex Method - Programming Problem

Maatttt0
Simplex Method --- Programming Problem

## Homework Statement

Here's the question -
Conside the linear programming problem:

maximise P = -3x + y,

subject to 3x + 2y =< 24,
4x + 9y =< 36,
-2x + y =< 1,
and x >= 0, y >= 0.

Represent the problem as an initial Simplex tableau and use the Simplex algorithm to solve the problem. Interpret your final tableau.

## The Attempt at a Solution

My problem is I'm usure how to tackle this with 3 subjects (ignoring the one with X and Y must be greater or equal to 0). I have completed questions in class with 2 subjects but my teacher nor my text book mention anything about 3 of them.

I attempted it a couple of times with just putting it in a follow the steps as I would with 2 subjects but it doesn't seem to work perfectly. Is this the correct way?

I would post my attempts but it'll get a bit complicated over the computer.

Mentor

The three inequalities are called constraints, not subjects. The idea is to maximize the objective function, subject to those constraints.

To get this ready to put into a simplex tableau, you need to add one slack variable for each of the three inequalities that involve both x and y. This turns each inequality into an equation.

For example, the first inequality becomes 3x + 2y + r = 24.

Maatttt0

Thank you for the reply but I understand that much. I'm unsure if there is a different idea for 3 constraints (I forgot the word earlier).

Maatttt0

I think I have worked it now - thank you all. :)

Mentor

No, it's the same no matter how many constraints you have - one row in the tableau for each constraint equation (i.e., the equation you get after adding a slack variable to the constraint inequality).

Once you get an answer, you can check by graphing the feasible region and confirming that the point you found maximizes the objective function.

Maatttt0

Thank you for clearing that up Mark :)