A general mathematical model is developed to specify the performance of an irreversible gas turbine Brayton cycle incorporating two-stage compressor, two-stage gas turbine, intercooler, reheater, and regenerator with irreversibilities due to finite heat transfer rates and pressure drops. Ranges of operating parameters resulting in optimum performance (i.e., h _I ³ 38 ³ h _II ³ 60%, ECOP ³ 1.65, x_loss £ 0.150 MJ/kg, BWR £ 0.525, w_net ³ 0.300 MJ/kg, and q_add £ 0.470 MJ/kg) are determined and discussed using the Monte Carlo method. These operating ranges are minimum cycle temperature ranges between 302 and 315 K, maximum cycle temperature ranges between 1,320 and 1,360 K, maximum cycle pressure ranges between 1.449 and 2.830 MPa, and conductance of the heat exchanger ranges between 20.7 and 29.6 kW/K. Exclusive effect of each of the operating parameters on each of the performance parameters is mathematically given in a general formulation that is applicable regardless of the values of the rest of the operating parameters and under any condition of operation of the cycle.