In this paper, we discuss the use of sequential quadratic programming to obtain the optimum feed rate strategy for the fed-batch operation of two biochemical systems: (I) lysine and (II) alcohol fermentation. We consider the constrained optimization problem where the reactor operation is such that the final volume is fixed. Both fixed and free time of operations are considered. In this approach, the entire duration of the reactor operation is divided into equal subintervals. The feed rate is approximated as discretized charges which are added to the reactor at the beginning of each subinterval. The effect of the number of stages on the optimum performance for both systems is investigated. The results are compared with those obtained using Pontryagin's maximum principle in the literature. The advantages and the applications of using this approach are discussed.In this paper, we discuss the use of sequential quadratic programming to obtain the optimum feed rate strategy for the fed-batch operation of two biochemical systems: (I) lysine and (II) alcohol fermentation. We consider the constrained optimization problem where the reactor operation is such that the final volume is fixed. Both fixed and free time of operations are considered. In this approach, the entire duration of the reactor operation is divided into equal subintervals. The feed rate is approximated as discretized charges which are added to the reactor at the beginning of each subinterval. The effect of the number of stages on the optimum performance for both systems is investigated. The results are compared with those obtained using Pontryagin's maximum principle in the literature. The advantages and the applications of using this approach are discussed.