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Wireless sensor networks (WSNs) are used to obtain information from the surrounding areas and collected data is reported to the base station through wireless links. In certain scenarios ongoing transmissions within the network need to be concealed so that no information is leaked beyond a vulnerable area. Such a concealment effort necessitates transmit ranges of radios to be limited. However, limiting transmit ranges results in sub-optimal routing patterns within the network, which results in lower network lifetime. In this paper, through a Linear Programming (LP) framework, we analyze lifetime limits of WSNs improving contextual privacy by transmit range control.