vIf a problem has only less-than-or-equal-to constraints with positive coefficients for the…

➤ How does rounding down affect the objective value in integer programming?
Rounding down keeps feasibility but can change the objective. For a maximization problem with nonnegative objective coefficients, the value will not increase and typically decreases. For minimization, the effect depends on objective signs. Rounding rarely yields an optimal integer solution without further adjustments.