In solving a maximization problem, the optimal profit associated with the relaxed solution (LP-relaxation) is always less than or equal to the value of the optimal profit associated with the integer solution.

Question

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In a maximization problem, the optimal profit of the LP-relaxation (where the integer constraints are relaxed to allow for fractional values) is always greater than or equal to the optimal profit of the integer solution, because the relaxation allows for a larger feasible region, potentially including solutions with higher profits that are not available in the integer-constrained version.

In Solving a Maximization Problem, the Optimal Profit Associated with the Relaxed