$\max Z = 6x_1 + 7x_2$


$-2x_1 + 2x_2 \le 3\\ 7x_1 + 3x_2 \le 22$

$x_1,x_2 \ge 0$ and $x_1, x_2 \in \Bbb Z$

How to solve this problem with relaxation LP by graphical method?


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  • $\begingroup$ Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. $\endgroup$ – José Carlos Santos Dec 5 '17 at 16:22
  • $\begingroup$ I have found that the optimal soluiton by Graphical Method is x1 = 1.75 and x2 = 3.25. $\endgroup$ – user3769812 Dec 5 '17 at 16:30
  • $\begingroup$ But I didnt understand what I need to do in this problem to find the relaxation solution $\endgroup$ – user3769812 Dec 5 '17 at 16:32
  • $\begingroup$ Is there some example of an non linear relaxation?? $\endgroup$ – user3769812 Dec 5 '17 at 18:06


$x_1 =3$, $x_2 =4$ doesn't satisfy one of your equations ($7x+3y \le 22)$.

The only integer values that satisfy the constraints are: $(x_1,x_2)=\{(0,0),(0,1),(1,0),(1,1),(1,2), (2,0),(2,1),(2,2),(3,0)\}$

  • $\begingroup$ Integer solution should be $(2,2)$. So, $Z=26$ $\endgroup$ – Albatross Dec 5 '17 at 17:07
  • $\begingroup$ Yes, that is right. $\endgroup$ – user3769812 Dec 5 '17 at 17:21
  • $\begingroup$ But What I need to do to find the relaxation solution by graphical method?? $\endgroup$ – user3769812 Dec 5 '17 at 17:21

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