In this paper we show that the thermodynamic performance of a gas turbine power plant cart be optimized by adjusting the flow rate and the distribution of pressure losses along the flow path. Specifically, we show that the power output has a maximum with respect to the fuel flow rate or any of the pressure drops, The maximized power output has additional maxima with respect to the overall pressure ratio and overall temperature ratio. When the optimization is performed Subject to a fixed fuel flow rate, and the power plant size is constrained the power output and efficiency can be maximized again by properly allocating the fixed total flow area among the compressor inlet and the turbine outlet.