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Wireless sensor networks are composed of energy-constrained nodes. Therefore, it is crucial to design routing algorithms that optimize the energy usage of nodes. Aimed at maximizing the network lifetime, we introduced an optimal routing algorithm based on the max-min model. In this algorithm, the data transmission matrix is defined and the relaying node selection mechanism is designed to avoid possible routing loops. Based on the energy consumption for sending and receiving data and the available residual energy of nodes, the mathematical programming model is designed to find optimal routing. The routing paths and data volume are determined by nodes according to the optimization of parameters in the model. Simulation results show that the algorithm balances the energy consumption of nodes effectively and extends the network lifetime.