# Branch and bound method in case the non integer value is less than 1.

If I need to find the integer valued solution to Linear programming problem using branch and bound method, but the non integer x value at the last iteration is less than 1, let's say 3/4. Then I have one constrain $$x_1 \le 0$$ and $$x_1 \ge 1$$. How do I proceed with the first case, when $$x_1 \le 0$$? I cannot add another constrain with auxiliary variable $$x_1 + s_1 \le 0$$, because all $$x_i \ge 0$$. Can I simply assume that $$x_1 = 0$$ and do the linear programming problem ignoring the $$x_1$$ variable?

• It´s better to post the whole problem and not only a part of it. Mar 4 at 16:07

If you started with nonnegative constraint and you branch on $$x_1 \le 0$$ and $$x_1 \ge 1$$, under that branch of $$x_1 \le 0$$ and $$x_1 \ge 0,$$ you can indeed conclude that $$x_1=0.$$