# Example of $c^Tx' = c^Tx$ where x is the optimal solution for the linear relaxation (LP) of x' (ILP)

I am looking for an example where the optimal solution for the LP problem is equal to the optimal solution of the ILP problem, but the solutions are different.

All I managed to think of was the example of the knapsack problem, when the sum of all the weights were less than W (max weight). However, in this solution x=x', and I was looking for an example in which they are different.

I am a computer science undergraduate so if you have something I may understand it would be much appreciated.

Thank you