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A wireless acoustic sensor network is envisaged that relies on a collection of spatially distributed microphones, which observe a speech signal together with additive background noise. The microphone signals are sent to a fusion center where they are filtered and combined to produce an estimate of the speech signal. In order to save energy and extend network lifetime, it is desired to only have a subset of the microphones active at any one moment. This subset selection unfortunately comes with the adverse effect of decreasing the accuracy of the signal estimation. Since the network now has two competing objectives a trade-off develops that balances the energy consumption to estimation accuracy. We propose a network model that is cast similarly to a 0-1 knapsack problem that uses a greedy method to balance the output signal-to-noise ratio to total transmission energy expended by the wireless microphones. Simulations show that although a greedy approach is used, a relatively small decrease in output signal-to-noise ratio is achieved while there is a marked decrease in energy usage of the system.