Linear programming problem using the simplex method. Max $P= 7x + 5y + 6z$

Subject to: $$x + y − z \le 3 x + 2y + z \le 8 x + y ≤ 5$$ $x \ge 0, y \ge 0, z \ge 0$

My try: I know how to solve by simplex method but here constraints are linked .So, plz just give me a hint so that could solve it.Thank you.

  • $\begingroup$ why don't you simplify $$x+y-z\le 3x+2y+z$$? $\endgroup$ – Dr. Sonnhard Graubner Feb 23 '17 at 17:27
  • $\begingroup$ There is also another one i.e $8x+y$. $\endgroup$ – MatheMagic Feb 23 '17 at 17:29

You could add dummy variables $u$ and $v$: \begin{cases} x+y-z \le u\\ 3x+2y+z \ge u \\ 3x+2y+z \le v \\ 8x+8y \ge v \\ 8x+8y \le 5 \end{cases}


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