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In the following paper, we study the tradeoff between network utility and network lifetime for energy-constrained wireless sensor networks (WSNs). By introducing a parameter r, we combine these two objectives into a single weighted objective, and consider rate control and routing in this tradeoff framework simultaneously. First, using the dual decomposition method, we decompose the tradeoff model into two subproblems: congestion control/routing problem and network lifetime problem, both of which interact through the dual variables for energy dissipation constraints. Based on decomposition results, we derive a partially distributed algorithm where the network lifetime is a global information. Second, we propose a fully distributed algorithm by approximating the network lifetime maximization problem by the network utility maximization (NUM) framework. Our algorithms are more competent for practical implementation than those of literatures, since we have considered more practical factors in our network model.