  A problem about how to transport profitably a group of cars leads us to study
the set $T$ formed by the integers $n$ such that the system of inequalities,
with non-negative integer coefficients,
  $$a_1x_1 +\cdots+ a_px_p + \alpha \leq n \leq b_1x_1 +\cdots+ b_px_p -
\beta$$ has at least one solution in ${\mathbb N}^p$. We will see that
$T\cup\{0\}$ is a submonoid of $({\mathbb N},+)$. Moreover, we show algorithmic
processes to compute $T$.
