# Exercise LP Relaxation [closed]

$\max Z = 6x_1 + 7x_2$

Constraints:

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

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

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

## closed as off-topic by Brian Borchers, Rolf Hoyer, Namaste, Shailesh, Parcly TaxelDec 6 '17 at 3:11

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• Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. – José Carlos Santos Dec 5 '17 at 16:22
• I have found that the optimal soluiton by Graphical Method is x1 = 1.75 and x2 = 3.25. – user3769812 Dec 5 '17 at 16:30
• But I didnt understand what I need to do in this problem to find the relaxation solution – user3769812 Dec 5 '17 at 16:32
• Is there some example of an non linear relaxation?? – 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: $(x_1,x_2)=\{(0,0),(0,1),(1,0),(1,1),(1,2), (2,0),(2,1),(2,2),(3,0)\}$
• Integer solution should be $(2,2)$. So, $Z=26$ – Albatross Dec 5 '17 at 17:07