Minimize $x_1+6x_2-x_3$ subject to $7x_1+x_2-x_3=6$, $3x_1+x_2+2x_3\leq 6$, $x_1,x_2\in\mathbb{R_+}$.
I first tried to represent $x_3$ in terms of $x_1$ and $x_2$, so $x_3=7x_1+x_2-6$, substituting this into the cost function: $\min\{x_1+6x_2-7x_1-x_2+6\}\iff \min\{-6x_1+5x_2+6\}$ subject to $3x_1+x_2+2(7x_1+x_2-6)\leq 6\iff 17x_1+3x_2\leq 18$; I'm kind of stuck here. Any pointers?