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In this paper, we address the problem of lifetime optimization under coverage and connectivity requirements for sensor networks where different targets need to be monitored by different types of 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, etc. First we formulate this NP-complete lifetime optimization problem, which is general and allows unprecedented diversity in coverage requirements, communication ranges, and sensing ranges. Our approach is based on column generation, where a column corresponds 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. To speed up the convergence rate, we generate an initial solution through a novel random selection algorithm. Through extensive simulations, we systematically study the effect of target priorities, communication ranges, and sensing ranges on the lifetime.