We study in this paper the optimization of a production system comprising a multi-item single machine. Taking into account the switching-costs, we analyze the optimization of the system in terms of a system of Quasi-Variational-Inequalities (QVI) which due to the presence of state restrictions, has unbounded solutions. This system represents the Bellman equation associated to this optimal switching control problem. We study the structure of this QVI system, its solutions and numerical methods to solve it.