We consider a well known mathematical model of continuous methane fermentation, consisting of two nonlinear ordinary differential equations and one algebraic equation for the gaseous output. The model involves one microbial population and one substrate. We propose an output feedback including a discrete delay and use it for asymptotic stabilization of the model. Feedback control of bioreactor models provides many advantages in operating a plant, mainly by increasing its efficiency. We also propose a numerical modelbased extremum seeking algorithm for maximizing the biogas (methane) flow rate in real time. Numerical simulations using this algorithm are included. The simulations are implemented in the Python programming language which is recently recognized as a powerful modern general purpose object-oriented language.