The optimization of batch and semibatch process operation is a natural choice for reducing production costs, improving product quality, and meeting safety and environmental regulations. The optimal solution can be implemented easily if it is determined by the constraints of the optimization problem; i.e., it is not inside the feasible region. For discontinuous two-reaction systems, this paper provides conditions that guarantee that the optimal temperature and feed-rate policies be determined by path constraints. It is shown that the optimal temperature profile is determined by a constraint if the desired reaction has a larger activation energy than the side reaction or if the side reaction tends to improve the objective function. Furthermore, for the majority of two-reaction schemes, the optimal feed rate is also determined by constraints. The optimal temperature and/or feed-rate profiles are computed numerically for three different examples in order to illustrate the theoretical developments.