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Network throughput and energy consumption are two important performance metrics for a multi-hop wireless network. Current state-of-the-art is limited to either maximizing throughput under some energy constraint or minimizing energy consumption while satisfying some throughput requirement. In this paper, we take a multicriteria optimization approach to offer a systematic study on the relationship between the two performance objectives. We show that the solution to the multicriteria optimization problem is equivalent to finding an optimal throughput-energy curve, which characterizes the envelope of the entire throughput-energy region. We prove some important properties of the optimal throughput-energy curve. For case study, we consider both linear and nonlinear throughput functions. In the linear case, we characterize the optimal throughput-energy curve precisely through parametric analysis, while in the nonlinear case, we use a piece-wise linear approximation to approximate the optimal throughput-energy curve with arbitrary accuracy. Our results offer important insights on exploiting the trade-off between the two performance metrics.