In the polymer industry, product quality is usually determined by the molecular weight distribution of polymer products. We propose a comprehensive study of polymer product design through dynamic optimization of average molecular weights and the polydispersity index in batch free radical polymerization. After analyzing and validating the modified Stickler-Panke-Hamielec (SPH) model, this paper extends the model to achieve product design with a specified polymer molecular weight distribution for various optimization goals. Conversion maximization under isothermal conditions was studied first. We concluded that dynamic optimization is useful to obtain desired products. However, some specifications of polymer molecular weight distribution cannot be achieved under isothermal conditions. Therefore, optimization with piecewise constant temperature profiles was also studied to extend the range of product specifications. Considering the practical requirement for productivity in engineering applications, reaction time minimization with specified conversion was studied with various temperature profiles. Besides the strategy of optimizing the temperature profile, dynamic optimization of initiator feed profiles is also presented. The results show that polymer product design with a specified polymer molecular weight distribution can be achieved using dynamic optimization of the temperature and initiator profiles in a batch reaction.