I am trying to understand how to solve minimisation problems using primal simplex method and somehow I understand the steps, just that the final result is not correct. Maybe I am doing something wrong. I have tried searching the net for detailed steps but I don't understand them. Precisely my problem is the tableau, I set it up (with slack variables) and I start by finding the pivot column that is smallest number in the objective function variables row, then I find the pivot row and then I make sure that the numbers in the pivot column (except the pivot number) are 0. I continue doing this until there are no negative numbers in the objective function row. It seems that doing these steps I can't find the correct result.
The problem is the following:
$$ z=-2x_1 + 2x_2 + 2x_3 $$ s.t $$x_1 + x_2 - 2x_3 \geq 1$$ $$x_1 + x_2 - x_3 \leq 3$$ $$-x_1 - x_2 +3x_3 \geq -2$$ $$x_1,x_2,x_3 \geq 0$$
EDIT: My solution
