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Recharging the batteries of a moribund sensor deployed as part of a wireless sensor network is often infeasible due to logistical considerations. With the purpose of prolonging sensor lifetime in such data-centric wireless sensor networks and with emphasis on TDMA-based routing and the efficient scheduling of sensor activities, we propose a mixed-integer nonlinear programming mathematical model, the objective of which is to minimize the total energy consumed by nodes and encompasses dynamic power range, collision free transmission, routing paths, and data aggregation tree constraints. Performing Lagrangean relaxation, we find a near-optimal solution and verify that our proposed algorithm is energy efficient and bounds latency within a reasonable range. Our experiment results confirm improvement over data aggregation algorithms.