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Power efficiency is an important design issue in embedded devices with limited power supplies. In this paper, we study a reward-based packet scheduling problem in wireless environments. We consider a general scenario in which a transmitter communicates with multiple receivers periodically. To guarantee timely transmission of data, each packet is associated with a delay constraint. The periodic data streams have different importance levels, power functions, and levels of data sizes. The more data a transmitter delivers, the more rewards it obtains. Our objective is to develop schemes that selectively transmit data streams of different data sizes at different transmission rates to maximize the system reward under given time and energy constraints. We show that this problem is NP-hard and develop a dynamic programming algorithm for the optimal solution in pseudo-polynomial time. A fast polynomial-time heuristic approach is presented to achieve close approximation. Simulation results demonstrate that the proposed heuristic approach can achieve a significant improvement over other approaches adapted from existing studies at a small runtime overhead.