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Since nodes in a sensor network have limited energy, prolonging the network lifetime and improving scalability become important. Therefore, the communication or message passing process must be designed to conserve the limited energy resources of the sensors. It is well known that clustering sensors into groups, so that sensors communicate information only to clusterheads and then the clusterheads communicate the aggregated information to the processing center, will save energy. However, no previous works have analyzed, from a theoretical perspective, the effect of careful assignment of energy supply to each node in multi-hop sensor networks. In this paper, we propose an analytical framework to quantify the impact of energy assignment to each node on the lifetime of sensor networks. We analyze the behavior of multi-hop routing and the total cost due to energy consumption on packet forwarding and network lifetime. Based on the total cost, we investigate the trade-off between energy saving and network lifetime. We show that the total cost is minimized by applying a scheme which allocates the initial energy supply of each node based on node distance from the data sink. We also show that network lifetime is increased dramatically in such optimum energy of node.