In all cases, though, the solution quality of the linear program is at least as good as that of the integer program, because any integer program solution would also be a valid linear program solution. That is, in a maximization problem, the relaxed program has a value greater than or equal to that of the original program, while in a minimization problem such as the set cover problem the relaxed program has a value smaller than or equal to that of the original program. Thus, the relaxation provides an optimistic bound on the integer program's solution.