The present research has analyzed the energy and exergy of a combined system of simultaneous power generation and cooling. To provide a comprehensive data sheet of this system, the system has been investigated in the temperature range of 300–800 °C, and 6 working fluids, including air, carbon dioxide, nitrogen, argon, xenon, and helium, have been investigated. The parameters affecting the performance of the system, namely the compressor inlet pressure, the compressor pressure ratio, and the intermediation pressure ratio were investigated. The power produced by the Brayton cycle at a pressure ratio of 5.2 is the highest due to the increase in compressor power consumption and turbine power generation. The results of the parametric study showed that the exergy efficiency of the system has the maximum value at the pressure ratio of 4.73. The results of the parametric study showed that increasing the pressure of the compressor does not have a significant effect on the electricity consumption and the temperature of the working fluid due to the constant pressure ratio. The input energy to the heat exchanger of the absorption chiller decreases with the increase in the Brayton cycle pressure ratio, and as a result, the cooling created by the chiller also decreases. In this method, three objective functions of exergy efficiency, energy efficiency, and total production power are considered as objective functions. The most optimal value of intermediation pressure ratio was obtained after the optimization process of 1.389. Also, the most optimal value of the pressure ratio of high-pressure and low-pressure turbines was reported as 2.563 and 1.845, respectively.