$(20$ points$)$ Find a feasible solution or determine that no feasible solu$-$

tion exists for the following system of difference constraints:

$x_1-x_{5}2$

$x_3-x_{4}0$

$x_5-x_2-4$

$x_2-x_{3}2$

$x_4-x_{1}11$

Include the graph constructed from the difference constraints model

in your solution.