Simplex method - infeasible(adsbygoogle = window.adsbygoogle || []).push({});

I'm looking at some linear optimization problems. In one example I must be missing something, maybe someone can point it out. Here's the example:

[tex]

\begin{align*}

\textrm{max } f(\textbf{x}) = & 2x_1 + x_2 \\

\textrm{subject to} & x_1 + x_2 \leq 5 \\

& -x_1 + x_2 \geq 1 \\

& \textbf{x} \geq 0

\end{align*}

[/tex]

When I try to perform iterations of the simplex method I get funky results, not feasible stuff. I suspect that it is due to how I set up my slack variables, ##x_3## and ##x_4##. My starting point ##x=(0,0)## is not in the feasible set, but that shouldn't matter, right?

[tex]

\begin{align*}

\textrm{min } f(\textbf{x}) = & -2x_1 - x_2 \\

\textrm{subject to} & x_1 + x_2 + x_3 = 5 \\

& x_1 - x_2 + x_4 = - 1 \\

& \textbf{x} \geq 0

\end{align*}

[/tex]

Are my slack variables wrong..? Or is it something else causing me to end up in infeasible points in my iterations?

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# Simplex method - infeasible

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