This paper outlines the thermodynamic optimization of a combined power and refrigeration system subject to constraints. In the first part, the system operates in the refrigeration mode and is driven by a hot stream of single-phase fluid that is subsequently discharged into the ambient. The irreversibility is due to three heat exchangers and the discharging of the used stream. It is shown that the thermodynamic optimum is pinpointed by an optimal ratio between the mass flow rates of the hot stream and the stream that is heated by the hot stream, and by an optimal distribution of the heat exchanger inventory among the three heat exchangers of the installation. The second part of the paper considers the more general situation where the system delivers power and refrigeration, and where the irreversibility is due additionally to the internal parts of the system. It is shown that the thermodynamic optimum is reached by distributing optimally the heat exchanger inventory among the three heat exchangers, and that this optimum is sensitive to the total inventory and the degree of irreversibility of the internal parts. It is also shown that the optimum is robust with respect to changes in several physical parameters.