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We extend the existing network utility maximization (NUM) framework for wired networks to wireless sensor networks by formulating it in order to take into account interference among radio links. We study the conditions under which the formulated problem is a feasible convex optimization problem. Under such conditions, a distributed algorithm is proposed to solve the problem optimally. Finally, we provide numerical results, based on computer simulations, to show the performance of the proposed algorithm and the rate of convergence of its solution.