(10%) Find a feasible solution or determine that no feasible solution exists for the following system of difference constraints:
x1−x3≤1x_1 - x_3 \le 1x1−x3≤1 x2−x3≤−4x_2 - x_3 \le -4x2−x3≤−4 x4−x5≤2x_4 - x_5 \le 2x4−x5≤2 x3−x4≤7x_3 - x_4 \le 7x3−x4≤7 x5−x1≤5x_5 - x_1 \le 5x5−x1≤5 x4−x2≤10x_4 - x_2 \le 10x4−x2≤10 x1−x2≤2x_1 - x_2 \le 2x1−x2≤2 x5−x3≤−1x_5 - x_3 \le -1x5−x3≤−1
