This paper presents a novel approach for upgrading utility systems by integrating absorption cooling systems using R-curve analysis. The key contributions include a comprehensive methodology for drawing the R-curve, determining priority paths, and optimizing the system without additional capital costs; a step-by-step case study illustrating the process of integrating two absorption chillers and analyzing their impact on cogeneration efficiency and the R-curve; equations for calculating cogeneration efficiency and power efficiency for different turbine paths to prioritize the most efficient paths; and findings revealing that integrating absorption chillers can significantly impact system performance, potentially increasing or decreasing cogeneration efficiency depending on the specific system. The proposed approach enables engineers to optimize utility systems by leveraging existing equipment and integrating absorption cooling efficiently, with the R-curve analysis providing a powerful tool for visualizing and optimizing the system to achieve the best balance of power, cooling, and heating. The findings demonstrate that careful analysis and optimization of the utility system using R-curve techniques can unlock significant energy savings and emissions reductions by prioritizing the most efficient turbine paths and integrating absorption cooling optimally.