In this study, we determine the operating conditions required to produce polymers with specific molecular weight distribution parameters in a continuous free radical polymerization reactor. Structural analysis of the mathematical model reveals that in the case of free radical polymerization that does not involve a termination-by-combination reaction, we cannot determine the set of operating conditions required for the production of polymers with a specific number-average molecular weight (M-n) and polydispersity index (PDI).