LAUSR

A problem about how to transport profitably a group of cars leads us to studying the set T formed by the integers n such that the system of inequalities, with non-negative integer coefficients, $$\begin{aligned} a_1x_1 +\cdots + a_px_p + \alpha \le n \le b_1x_1 +\cdots + b_px_p - \beta \end{aligned}$$a1x1+⋯+apxp+α≤n≤b1x1+⋯+bpxp-βhas at least one solution in $${\mathbb N}^p$$Np. We prove that $$T\cup \{0\}$$T∪{0} is a submonoid of $$({\mathbb N},+)$$(N,+) and, moreover, we give algorithmic processes to compute T.