Biotechnological production of a recombinant molecules relies heavily on fed-batch processes. However, as the cells' growth, substrate uptake, and production kinetics are often unclear, the fed-batches are frequently operated under sub-optimal conditions. For example, process designs are based on simple feed profiles (e.g., constant or exponential), operator experience, and basic statistical tools like response surface methodology (RSM), which are unable to harvest the full potential of the production processes. To address this challenge, we propose a general modeling framework, OptFed, which utilizes experimental data from non-optimal fed-batch processes to predict an optimal process. In detail, we assume the cell-specific production rate depends on all state variables and their changes over time. Using measurements of bioreactor volume, biomass, and product, we train an ordinary differential equation model. To avoid overfitting, we use a regression model to reduce the number of kinetic parameters. Then, we predict the optimal process conditions (temperature and feed rate) by solving an optimal control problem using orthogonal collocation and nonlinear programming. We apply OptFed to a recombinant protein L fed-batch production process. We determine optimal controls for feed rate and reactor temperature to maximize the product-to-biomass yield and successfully validate our predictions experimentally. Notably, our framework outperforms RSM in both simulation and experiments, capturing an optimum previously missed. We improve the experimental product-to-biomass ratio by 19 % and showcase OptFed's potential for enhancing process optimization in biotechnology.