In this paper, the possibility of enhancing selectivity in parallel-series reaction networks using different reactant feeding strategies is investigated theoretically. Isothermal tubular reactors are considered where reactants can be introduced at the entrance and also added over the wall. The latter method of dosing can be realized, for example, in a membrane reactor. The control variable considered is the dosing profile of a reactant along the wall. As a typical objective function, the mole fraction of a desired intermediate product at the reactor outlet is maximized. The optimal profile is calculated analytically under some assumptions using Pontryagin's maximum principle. The results enable us to understand how the different variables determine the control policy. Insight from this approach is subsequently used to determine numerically the optimal profiles using sequential quadratic programming under more general conditions.