The Constraint-based modelling is a widely used approach to analyze genotype-phenotype relationships. The main key concepts are stoichiometric analysis such as flux balance analysis (FBA), Resource Balance Analysis (RBA) or elementary flux mode (EFM) analysis. While FBA identifies optimal flux distribution with respect to a given objective, the EFM characterizes the totality of the available solution space in terms of minimal pathways but their number leads to a combinatorial explosion for large networks. The RBA predicts for a specific environment, the set of possible cell configurations compatible with the available resources and extends very significantly the predictive power of the FBA. However, when stoichiometric and kinetic constraints are considered together, the set of possible flux configurations does not generally define a convex set since the kinetic function are not linear. The problem resolution has thus multiple local maxima. Recent works showed that the optimal solution of constraint enzyme allocation problems with general kinetics is an EFM. Based in this recent outcome, we write the resource allocation constraint on kinetic optimization problem into a geometric problem in an EFM, i.e. a convex optimal problem easily solved. Thus to predict optimal flux modes, we compute constraints EFMs with our tool ASPefm based on Answer Set Programming to save time and space computation. ASPefm allows the integration of Boolean and linear constraints such as thermodynamic, environment, transcriptomic regulatory rules, and resource operating cost (that identify the most efficient EFMs for converting substrate into biomass) using the solver ClingoLP which combined logic programming and linear programming. The convex optimization problem is then resolved on each constraint EFMs which provides for this mode, the optimal repartition of resources among enzymes and the associated metabolite concentrations. We applied our method to the central carbon metabolism of E. coli, with a detailed model of the respiration chains, ATPase (including explicitly the proton motive force). The optimal flux mode is the overflow of acetate which is in agreement with known experimental results. This approach allowed us to explore whether certain experimental properties observed on E. coli are consistent and consequences of an optimal repartition of bacterial resources. Our method is very promising in synthetic biology and increased the ability to efficiently design biological systems.