The IP solution can sometimes produce a better objective function value than its LP relaxed problem.

Question

Quizplus · Accepted Answer

The LP relaxation of an IP problem allows for fractional values, which broadens the feasible region. Therefore, the optimal solution to the LP relaxation provides a bound (either lower or upper, depending on the nature of the optimization) to the IP problem but cannot yield a better objective function value than the optimal integer solution.

The IP Solution Can Sometimes Produce a Better Objective Function