I want to solve the following linear programming problem by graphical method :

$$\text{Minimize}\quad Z=0.4x_1+0.5x_2,$$ Subject to $$0.3x_1+0.1x_2\le2.7$$ $$0.5x_1+0.5x_2=6$$ $$0.6x_1+0.4x_2\ge6$$ and, $$x_1\ge0,x_2\ge0$$

The book which I am following also shows the graph : enter image description here

But I am not understanding how did they draw the graph ? Say, for example, how did they draw the line for $0.3x_1+0.1x_2\le2.7$ and $0.5x_1+0.5x_2=6$ ?


Hint: Rearrange the equations into the form $x_2\leq mx_1+c$

  • $\begingroup$ If I rewrite $0.3x_1+0.1x_2\le2.7$, it becomes $x_1\le 9-(1/3)x_2$. What to do next ? How can I draw the line ? $\endgroup$ – ABC Sep 22 '15 at 1:08
  • 1
    $\begingroup$ Id suggest doing some quick background reading on graphing linear equations and inequalities. mathwarehouse.com/algebra/linear_equation/linear-inequality.php $\endgroup$ – Nik-D Sep 22 '15 at 1:26

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