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.

Homework Equations

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 textbook 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.

Thank you in advance :)

 

[Mark44]

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. :)

 

[Mark44]

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 :)