Cognitive radio system is one of the viable solutions for effective spectrum management. Cooperative spectrum sensing is very often used to mitigate the challenge of interference encountered in single sensing systems. This paper is aimed at developing a model to determine the required number of cognitive radios that would optimize the performance of a communication network with respect to energy utilization and bandwidth requirement. Energy detection was used as the cognitive radio sensing technique due to the limited energy, computational and communication resources required. The noise variance of the channel was set to -25dB. Spectrum sensing was carried out at a frequency of 936MHZ and a bandwidth of 200kHz. Enhancement in specificity of the detection was also explored using machine learning in order to minimize interference. Genetic Algorithm (GA) was used to optimize the number of cognitive radios putting into consideration all constraints in the network. The optimization produced an overall reduction of 59.26% in energy conserved without compromising the detection accuracy.