If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables,rounding down will always provide a feasible integer solution.

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If all constraints have less-than-or-equal-to inequalities with positive coefficients, rounding down all variables will never violate any constraints since it will always result in a smaller but still valid solution. Therefore, rounding down will always provide a feasible integer solution.

If a Problem Has Only Less-Than-Or-Equal-To Constraints with Positive Coefficients