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I need to solve the following LPP using graphical method

Min $z=4x_1+x_2$

subject to $2x_1+x_2 \geq 2$,

$x_1+3x_2 \leq 4$,

$x_2 \leq 4$,

$x_1, x_2 \geq 0$

But I am not finding any common feasible region. Particularly from the figure we see that there is no common area to first two constraints . How to proceed?

  • $\begingroup$ Note that $x_2\le 4$ is not really necessary, since it is already covered by the first two conditions. What have you tried so far? $\endgroup$ – AugSB Mar 10 '16 at 11:47
  • $\begingroup$ I have included my attempts as an image file. $\endgroup$ – user3575652 Mar 11 '16 at 5:34
  • $\begingroup$ Are you sure that is the right plot? I got something different. $\endgroup$ – Ethan Hunt Mar 11 '16 at 6:16
  • $\begingroup$ Oh! really very sorry. It was a blunder $\endgroup$ – user3575652 Mar 11 '16 at 6:40

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