Production of monoclonal antibodies (mAbs) is a well-known method used to synthesize a large number of identical antibodies, which are molecules of huge importance in medicine. Due to such reasons, intense efforts have been invested to maximize the mAbs production in bioreactors with hybridoma cell cultures. However, the optimal control of such sensitive bioreactors is an engineering problem difficult to solve due to the large number of state-variables with highly nonlinear dynamics, which often translates into a non-convex optimization problem that involves a significant number of decision (control) variables. Based on an adequate kinetic model adopted from the literature, this paper focuses on developing an in-silico (model-based, offline) numerical analysis of a fed-batch bioreactor (FBR) with an immobilized hybridoma culture to determine its optimal feeding policy by considering a small number of control variables, thus ensuring maximization of mAbs production. The obtained time stepwise optimal feeding policies of FBR were proven to obtain better performances than those of simple batch operation (BR) for all the verified alternatives in terms of raw material consumption and mAbs productivity. Several elements of novelty (i-iv) are pointed out in the -conclusions‖ section (e.g., considering the continuously added biomass as a control variable during FBR).