In this paper, we introduced the concept of maximizing the Throughput of the system while maintaining optimum signal-to-interference ratios (SIR) by means of optimizing the powers between the terminals inside the cellular system. We have looked at network in which different terminals are assigned unequal transmission priorities and tried to optimize the overall throughput while maintaining equal signal-to interference ratio by way of power control of the transceivers. Optimization technique was used to derive the mathematical models for simulation.