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In this paper, we address the problem of lifetime maximization under coverage and connectivity requirements for heterogeneous wireless sensor networks where different targets need to be covered (sensed ) by different types of wireless sensors running at possibly different sampling rates as well as different initial energy reserve. The problem is particularly challenging since we need to consider both connectivity requirement and so-called target Q-coverage requirement, i.e., different targets may require different sensing quality in terms of the number of transducers, sampling rate, sensing data rate, etc. In this paper, we formulate a lifetime maximization problem, which is general and allows unprecedented diversity in coverage requirements, sampling rates, transmission energy consumption models, communication ranges, and target sensing ranges. Our approach is based on column generation, where a column corresponding to a feasible solution; our idea is to find a column with steepest ascent in lifetime, based on which we iteratively search for the maximum lifetime solution. Through extensive simulations, we systematically study the effect of sampling rates, transmission energy consumption models, communication ranges, and target sensing ranges on the lifetime.