Entropy generation minimization technique is used in the analysis of an irreversible closed intercooled regenerative Brayton cycle coupled to variable-temperature heat reservoirs. Mathematical models are developed for dimensionless power and efficiency for a multi-stage Brayton cycle. The dimensionless power and efficiency equations are used to analyze the effects of total pressure ratio, intercooling pressure ratio, thermal capacity rates of the working fluid and heat reservoirs, and the component (regenerator, intercooler, hot-and cold-side heat exchangers) effectiveness. Using detailed numerical examples, the optimal power and efficiency corresponding to variable component effectiveness, compressor and turbine efficiencies, intercooling pressure ratio, total pressure ratio, pressure recovery coefficients, heat reservoir inlet temperature ratio, and the cooling fluid in the intercooler and the cold-side heat reservoir inlet temperature ratio are analyzed.