This work considers the production of Polymethyl methacrylate (PMMA) to achieve target quality variables such as number and weight average molecular weights. A dynamic multiple-model based approach is first used to capture the process dynamics using data generated from a detailed first principles model. Subsequently, the multiple-model is integrated with a quality model to enable predicting the end quality based on initial conditions and candidate control input (jacket temperature) moves. A data-driven model predictive controller is then designed to achieve the desired product quality while satisfying input and a lower bound on the conversion, as well as additional constraints that enforce the validity of data-driven models for the range of chosen input moves. Simulation results demonstrate the superior performance (10.4% and 6.5% relative error in number average and weight average molecular weight compared to 19.8% and 18.5%) of the controller over traditional trajectory tracking approaches.