In this work we analyze the operation of a biochemical reactor in the nonrepeated fed-batch mode. The reaction is assumed to follow Haldane kinetics (i.e., it is characterized by substrate inhibition). The feed rate of the substrate is chosen as the control variable. We optimize the system performance using Pontryagins' maximum principle to obtain the flow rate profile F(t) for a nonlinear objective function. This is done without imposing any constraints on F(t) for the following cases: (1) fixed final volume, fixed final time; (2) free final volume, fixed final time; (3) fixed final volume, free final time; and (4) free final time, free final volume. The objective here is to maximize the biomass production such that the deviation from an average flow rate is minimal. This renders the problem nonsingular. The results of the optimal profile are compared with a semibatch reactor when a constant flow rate is maintained and also with the performance of a batch reactor. The effect of initial conditions on the different shapes of the optimal profiles is also discussed.In this work we analyze the operation of biochemical reactor in the nonrepeated fed-batch mode. The reaction is assumed to follow Haldane kinetics (i.e., it is characterized by substrate inhibition). The feed rate of the substrate is chosen as the control variable. We optimize the system performance using Pontryagins' maximum principle to obtain the flow rate profile F(t) for a nonlinear objective function. This is done without imposing any constraints on F(t) for the following cases: (1) fixed final volume, fixed final time: (2) free final volume, fixed final time; (3) fixed final volume, free final time; and (4) free final time, free final volume. The objective here is to maximize the biomass production such that the deviation from an average flow rate is minimal. This renders the problem nonsingular. The results of the optimal profile are compared with a semibatch reactor when a constant flow rate is maintained and also with the performance of a batch reactor. The effect of initial conditions on the different shapes of the optimal profiles is also discussed.