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How can I turn this into canonical form and then use the two-phase simplex method to solve it? Would I need to add slack variable AND surplus variables?

$$\max\quad -2x_1-x_2-x_3 \\ \text{subject to: }-x_1-x_3 \le -1 \\ -x_1+x_2 \le -2 \\ -x_2+x_3 \le -1 \\ x_1,x_2,x_3 \ge 0 $$

When I put it into the tableau with only slack variables there are no negative coefficients in the bottom room to find the column to pivot around.

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  • $\begingroup$ Anyone have any ideas? $\endgroup$ – Jackson Do Sep 3 '17 at 12:40
  • $\begingroup$ Yes, you have to add slack variables to make it a canonical form, then add artificial variables for each constraint so that in each constraint, there's one slack variable and one artificial variables. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Dec 18 '17 at 19:18

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