I am trying to implement a simplex algorithm for solving LP task. I will post the question and my solution as well - what I need to know is whether my solution is correct, thanks in advance!
criterial function $min(x_1 - x_2 + 2x_3)$ subject to: $-3x_1 + x_2 + x_3 = 4$. $x_1 - x_2 + x_3 = 3$, $\forall x_i \geq 0$.
My simplex table (I added two slack variables in order to create a starting base):
1 -1 2 0 0 | 0 .................. -3 1 1 1 0 | 4 1 -1 1 0 1 | 3
I chose 1 (position 2,2) as pivot and made one step of algorithm:
-2 0 3 1 0 | 4 .................. -3 1 1 1 0 | 4 -2 0 2 1 1 | 7
Now the first column in my table is negative -> this task cant be solve because X an open set (not sure if I can say it like this, dont know english notation that well) and minimum is -infinity.
Is this correct assumption or am I doint it wrong. Thanks...