New differential equations are derived for optimal control of a consecutive reaction system in a batch reactor. These equations can be solved easily with a one-dimensional optimum search technique in terms of the initial concentrations of each component. The computations are readily carried out on-line in real time, and the optimal temperature profile can be calculated at each time-step based on the current values of the states. Optimization is considered in terms of the temperature, but also in terms of an operation variable. For a consecutive reaction system, the optimal equations are formulated and optimal profiles are numerically calculated.