Many systems, such as domestic residences and business, institutional or shopping building complexes, require both a power input and a heat input to properly operate. Usually, the power input is in the form of electricity. An analysis for determining the most advantageous method of satisfying the energy requirements for these types of systems and of estimating the maximum possible value of the energy utilization factor is developed using an idealized regeneration cycle with heat exchangers that operate between different temperature reservoirs. The results are summarized in terms of the ratio of the heat load to the required power, (HLRP). The HLRP ratio is the significant design factor for these system and all results are scalable with it. The first law thermal efficiency or energy utilization factor and the entropy generation rate, (EGR), are determined at different practical operating conditions. The EGR is directly proportional to the rate of exergy destruction because of the system definition used in the analysis. The usefulness of the thermal efficiency and the EGR as design tools is investigated. The first law thermal efficiency reaches a maximum possible value of 76% at a HLRP ratio value of 0.67 for practical values of the operating conditions. At this HLRP ratio value the heat rejected from the heat engine equals the required heat load, the critical HLRP value. No minimum behavior was observed for the EGR as a function of the HLRP ratio for the cogeneration system. The EGR results are not a useful design tool during the initial design phase for cogeneration systems because of this trend. The results suggest that cogeneration systems should be selected for HLRP ratio values that are greater than the critical value. As the HLRP ratio increases the performance of the cogeneration system approaches that of the traditional system and are in an operating range that is governed by cost factors rather than energy usage factors. The results are compared to irreversible heat engine system and to a system without cogeneration. This research is the only first step of an investigation that will include the cost analysis and comparison to operating cogeneration installations in the next phase.