Part II of this paper develops the mathematical formulations of three applications of the thermoeconomic analysis methodology described in Part I of the paper: the operation diagnosis study, including new, concepts that helps to separate different contributions to those inefficiencies; the local optimization process in case of special conditions for the whole plant, and the benefit maximization (a direct application of the exergy costs accounting analysis). The operation diagnosis, which is the most complex and sophisticated application, is presented with the help of an example: the co-generation plant, as it was described in Part I.