Help is needed, I've tried to solve it by myself but I could find any reasonable solution which is solid enough. this is what I've wrote:
Consider a 0-1 ILP, where each variable x1,x2...,xn can assume values 0 or 1. The number of constraints is m.
We can choose all possible 2n assignments of x1, x2...xn in non-deterministic manner.
Checking the feasibility of each assignment takes O(nm) time, and Computing the value of the objective function for each feasible assignment takes O(n) time Since a nondeterministic manner considers all assignments simultaneously. Thus, we have a non-deterministic polynomial time.
Due to Karp
Please provide a better solution