An irreversible regenerative Brayton cycle model with two heat additions is analyzed here. The external irreversibilities due to finite temperature difference and internal irreversibilities due to fluid friction losses in compressor / turbine, regenerative heat loss, pressure loss are included in the analysis. Power output of the model is obtained and thermodynamically optimized. A detailed analysis shows that with judicious selection of parameters viz. efficiency of turbine and compressor, effectiveness of various heat exchangers, isothermal pressure drop ratio, pressure drop recovery coefficients and heat capacitance rate of the working fluid, the power output of the model can be made to reach its highest possible value. It is well proven with the obtained results that induction of two heat additions significantly enhances model efficiency above 20% as compared to conventional gas power plants. The power output remains constant while the corresponding thermal efficiency increases as regenerator side effectiveness is increased. This meticulous result is different from those obtained by previous researchers. The model analyzed in this paper gives lower values of power output and corresponding thermal efficiency as expected and replicates the results of an irreversible regenerative Brayton cycle model discussed in the literature at pressure recovery coefficients of α1=α2=1.