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The rapid proliferation of wireless sensor networks has stimulated enormous research efforts that aim to maximize the lifetime of battery-powered sensor nodes and, by extension, the overall network lifetime. Most work in this field can be divided into two equally important threads, namely (i) energy-efficient routing that balances traffic load across the network according to energy-related metrics and (ii) sleep scheduling that reduces energy cost due to idle listening by providing periodic sleep cycles for sensor nodes. To date, these two threads are pursued separately in the literature, leading to designs that optimize one component assuming the other is pre-determined. Such designs give rise to practical difficulty in determining the appropriate routing and sleep scheduling schemes in the real deployment of sensor networks, as neither component can be optimized without pre-fixing the other one. This paper endeavors to address the lack of a joint routing-and-sleep-scheduling scheme in the literature by incorporating the design of the two components into one optimization framework. Notably, joint routing-and-sleep-scheduling by itself is a non-convex optimization problem, which is difficult to solve. We tackle the problem by transforming it into an equivalent Signomial Program (SP) through relaxing the flow conservation constraints. The SP problem is then solved by an iterative Geometric Programming (IGP) method, yielding an near optimal routing-and-sleep-scheduling scheme that maximizes network lifetime. To the best of our knowledge, this is the first attempt to obtain the optimal joint routing-and-sleep-scheduling strategy for wireless sensor networks. The near optimal solution provided by this work opens up new possibilities for designing practical and heuristic schemes targeting the same problem, for now the performance of any new heuristics can be easily evaluated by using the proposed near optimal scheme as a benchmark.