Optimal control strategies for maximizing the production of induced foreign protein by recombinant bacteria were sought by the optimal control theory. Nutrient and inducer feeding rates were selected as key control variables. Since the problem is linear in the control variables, the optimal control is bang-bang or singular. Singular solutions are shown to exist. The optimal control theory showed that the specific growth rate with respect to nutrient concentration must be kept in its maximum phase and that there exist both a cell growth period and a protein production period. The optimal control theory calculates exactly the growth and production periods. The glucose concentration is controlled along a singular arc to give a maximum specific growth rate. The inducer level is controlled along a separate singular arc.