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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?

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    What is the domain of your variables? $\mathbb{Z}$ or $\mathbb{R}$ or something more exotic?2012-04-19
  • 0
    sorry -- it's $\mathbb{R}$.2012-04-19

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