(Operations research question and answer about square root bound)[https://or.stackexchange.com/q/678/671]
If only the variable bounds would agree with the numerators of the Dirichlet inverse of the Euler totient function expansion of the partial sums of the Möbius inverse of the Harmonic numbers, it would be the Riemann hypothesis. But they don't, unless there is some reason why only negative numbers in the variable bounds need to be considered in the linear programming problem.