This paper presents a dynamic optimization numerical case study for Monoclonal Antibody (mAb) production. The fermentation is conducted in a continuous perfusion reactor. We represent the existing model in terms of a general modeling methodology well-suited for simulation and optimization. The model consists of six ordinary differential equations (ODEs) for the non-constant volume and the five components in the reactor. We extend the model with a glucose inhibition term to make the model feasible for optimization case studies. We formulate an optimization problem in terms of an optimal control problem (OCP) and consider four different setups for optimization. The optimization results show that optimal operation of the continuous perfusion reactor increases the mAb production with up to 52% compared to the base case. Additionally, our results show that multiple optimal feeding trajectories exists and that full glucose utilization can be forced without loss of mAb formation.