We show preliminary results addressing the problem of resource allocation in bacteria in the continuous bioreactor framework. We propose a coarse-grained self-replicator dynamical model that accounts for the microbial population growth inside a continuous bioreactor, and we study its asymptotic behavior through a dynamical systems analysis approach, in order to provide conditions for the persistence of the bacterial population. We then study the two most relevant cases of steady-state production in this scheme: 1) biomass production, classical in high-tech industrial processes as well as in research environments; and 2) metabolite production through the introduction of a heterologous metabolic pathway. Both problems are explored in terms of the internal allocation control-which can be externally disrupted-and the constant volumetric flow of the bioreactor; and analyzed through a numerical approach. The resulting two-dimensional optimization problem is defined in terms of Michaelis-Menten kinetics using the parameter values of previous works, and taking into account the constraints for the existence of the equilibrium of interest.