I. INTRODUCTION
Symbiosis is a concept employed to describe organisms living in a close association [1]; mutualism is a type of symbiosis that has been described as the interaction of species in which they obtain benefits from each other [2], [3]. In [4] an instance of mutualism (syntrophy) was modeled and analysed, in the syntrophic case at least one of the organisms can grow without the other. Examples of mutualism are found in plants and seed dispersers [5], or metabolic cross-feeding [6], defined as the interaction in which a bacteria consumes the metabolite produced by another bacteria. In this article we present the model, analysis and optimization of two bacteria under metabolic cross-feeding in a chemostat.