On a transport problem and monoids of non-negative integers

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, a1x1 + center dot center dot center dot + apxp + a = n = b1x1 + center dot center dot center dot + bpxp - ss has at least one solution in . We prove that is a submonoid of and, moreover, we give algorithmic processes to compute T.