Multiple combinations of hardware and network components can be selected to design an information technology (IT) infrastructure that satisfies performance requirements. The professional criterion to deal with these degrees of freedom is cost minimization. However, a scientific approach has been rarely applied to cost minimization and a rigorous methodological support to cost issues of infrastructural design is still lacking. The methodological contribution of this paper is the representation of complex infrastructural design issues as a set of four intertwined cost-minimization sub-problems: two set-coverings, a set-packing and a min k-cut with a non linear objective function. Optimization is accomplished by sequentially solving all sub-problems with a heuristic approach and finally tuning the solution with a local-search approach. The methodology is empirically verified with a software tool including a database of costs that has also been built as part of this research. The work shows how an overall costminimization approach can provide significant savings and indicates how corresponding infrastructural design rules can substantially differ from the local optima previously identified by the professional literature.