# On a transport problem and monoids of non-negative integers

Research paper by Aureliano M. Robles-Pérez, José Carlos Rosales

Indexed on: 08 Nov '16Published on: 08 Nov '16Published in: arXiv - Mathematics - Group Theory

#### Abstract

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 $T$.