A method is described for determining the limits of number-average molecular weights, polydispersities, monomer conversions, residual initiator concentrations, and reactor network residence times that are possible in isothermal polymerizations. The general approach provides a visual representation of the "attainable region" and reactor networks which achieve the attainable limits. The approach is based on an extension of the work of Glasser et; al. (1987) to polymerization systems and is illustrated with a specific example of the free-radical polymerization of poly(methyl methacrylate), The results show how design conditions affect the range of attainable number-average molecular weights; the results indicate that; much higher molecular weights than those typically produced in industry are feasible. The results also demonstrate that while many reactor networks can produce a desired molecular weight, only a few carefully selected networks can yield the narrowest molecular weight distributions, These include a CSTR reactor, a CSTR reactor with a bypass feed stream, and a CSTR reactor followed by a PFR reactor.