Max $P= 7x + 5y + 6z$ Subject to: $x + y − z ≤ 3 x + 2y + z ≤ 8 x + y ≤ 5 x ≥ 0, y ≥ 0, z ≥ 0$

Question

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.

Answer 1

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}