Cutting plane in IP system

Question

I am doing branch-and-bound for 5 decision binary variables. so Decision would be 0 and 1. and I found sub-problem node Q with optimal value 5.4 (0.3, 0.2, 1, 0.5, 0.1)

my IP constraints are

x1 + 2x2 + x3   <= 4
2x1 + 3x2 + x3  <= 3
x1 + x2 + 2x3 + x4 <= 3 

how can I find "cutting plane" that makes Q solution infeasible ?

I need to recompute optimal solution for Q after introducing cutting plane but this is next step.

Should I introduce some slack variables ?

Answer 1

E.g. consider the second constraint. If $x_2 = 0$, $2 x_1 + x_3 \le 3$ is true (with $0 \le x_1, x_3 \le 1$, but if $x_2 = 1$, you must have $x_1 = 0$ and $x_3 = 0$. Thus $x_1 + x_2 \le 1$ and $x_2 + x_3 \le 1$ are possible cutting planes.