A combined power and Cooling cycle is being investigated. The cycle is a combination of the Rankine cycle and an absorption refrigeration cycle. Evaluating the efficiency of this cycle is made difficult by the fact that there are two different simultaneous outputs, namely cycle is made difficult by the fact that there are two different simultaneous outputs, namely power and refrigeration. An efficiency expression has to appropriately weigh the Cooling component in order to allow comparison of this cycle with other cycles. This paper develops several expressions for the first law, second law, and exergy efficiency definitions for the combined cycle based on existing definitions in the literature. Some of the developed equations have been recommended for use over others, depending on the comparison being made. Finally, some of these definitions have been applied to the cycle and the performance of the cycle optimized for maximum efficiency. A Generalized Reduced Gradient (GRG) method was used to perform the optimization. The results of these optimizations are presented and discussed.