In this work, the stoichiometric metabolic network of Escherichia coli has been formulated as a comprehensive mathematical programming model, with a view to identifying the optimal redirection of metabolic fluxes so that the yield of particular metabolites is maximized. Computation and analysis has shown that the over-production of a given metabolite at various cell growth rates is only possible for a finite ordered set of metabolic structures which, in addition, are metabolite-specific. Each regime has distinct topological features, although the actual flux values differ. Application of the model to the production of 20 amino acids on four carbon sources (glucose, glycerol, lactate, and citrate) has also indicated that, for fixed cell composition, the maximum amino acid yield decreases linearly with increasing cell growth rate. However, when the cell composition varies with cell growth rate, the amino-acid yield varies in a nonlinear manner. Medium optimization studies have also demonstrated that, of the above substrates, glucose and glycerol are the most efficient from the energetic viewpoint. Finally, model predictions are analyzed in the light of experimental data.