Bacterial responses to environmental changes rely on a complex network of biochemical reactions. The properties of the metabolic network determining these responses can be divided into two groups: the stoichiometric properties, given by the stoichiometry matrix, and the kinetic/thermodynamic properties, given by the rate equations of the reaction steps. The stoichiometry matrix represents the maximal metabolic capabilities of the organism, and the regulatory mechanisms based on the rate laws could be considered as being responsible for the administration of these capabilities. Post-genomic reconstruction of metabolic networks provides us with the stoichiometry matrix of particular strains of microorganisms, but the kinetic aspects of in vivo rate laws are still largely unknown. Therefore, the validity of predictions of cellular responses requiring detailed knowledge of the rate equations is difficult to assert. In this paper, we show that by applying optimisation criteria to the core stoichiometric network of the metabolism of Escherichia coli, and including information about reversibility/irreversibility only of the reaction steps, it is possible to calculate bacterial responses to growth media with different amounts of glucose and galactose. The target was the minimisation of the number of active reactions (subject to attaining a growth rate higher than a lower limit) and subsequent maximisation of the growth rate (subject to the number of active reactions being equal to the minimum previously calculated). Using this two-level target, we were able to obtain by calculation four fundamental behaviours found experimentally: inhibition of respiration at high glucose concentrations in aerobic conditions, turning on of respiration when glucose decreases, induction of galactose utilisation when the system is depleted of glucose and simultaneous use of glucose and galactose as carbon sources when both sugars are present in low concentrations. Preliminary results of the coarse pattern of sugar utilisation were also obtained with a genome-scale E. coli reconstructed network, yielding similar qualitative results.