I have the following LP problem (from Bazaraa, Jarvis and Sherali Linear Programming and Network Flow problem 1.30):
Minimize $x_1 - 2x_2 + 3x_3$
s.t. $-x_1+3x_2+x_3 \le13$
$ x_1+2x_2+3x_3 \ge 12 $
$2x_1-x_2+x_3 = 4$ $x_3 \le -3$
I need to convert this into standard and canonical forms for the exercise. To convert to standard form I have added two slack variables $s_1$ and $s_2$. This is what I have so far:
However, I am unsure what to do about the nonnegativity constraint that I need to add. I.e. $x_1$ and $x_2$ are not sign restricted and $x_3$ has another condition. How do I go about ensuring that all of my variables are nonnegative to fit the standard form?