The operating strategy that produces the maximum foreign protein expression for a fed-batch process is desired. This is achieved by using a feasible quadratic programming (FSQP) algorithm with a structured model that describes cell growth and product formation for recombinant E. coli. Optimization calculations for a fed-batch culture have not been performed with a model of this complexity up to this point. A constraint on the maximum cell concentration was included. For a fixed value of batch time, the results show that the optimal time profile of feed flow rate can increase the yield of foreign protein by 12-29% over a constant feed rate policy. Also, it was found that the computation time for the FSQP algorithm can be reduced significantly by considering suboptimal profiles of the feed rate, with a minor effect on calculated protein yield.