This paper presents the design using geometric programming of a merged CMOS LNA-Mixer cell, intended for bluetooth application at 2.45GHz. A rigorous noise formulation taking into account on chip inductors non-idealities and parameters from inductor measurement results is provided. Design considerations to achieve geometric programming suitable expressions for noise, gain, and input matching, among others, are presented. As a result, the designed LNA-Mixer cell exhibits a single side band noise figure of 9.64dB, with a voltage gain of 21.5dB, input reflection co-efficient S11 of -28.7dB, in addition to a PIIP3=-2.06dBm. The circuit area is 0.93mm2 and consumes 8.67mW at 3.3V power supply in a 0.35μm CMOS process.