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In this paper, we solve the resource allocation problem of maximizing the sum of transmitter utilities subject to QoS and peak power constraints per link in a wireless multihop network. Each node in the network has an associated utility function that models its valuation of its data rate (or signal power) in terms of its transmission power and multiaccess interference. By explicitly accounting for multiaccess interference in the utility function, our framework can model and solve a wide variety of resource allocation problems. Each link in the network is subject to a minimum and a maximum data rate constraint and each transmitter is subject to a peak power constraint. We present an iterative power control algorithm that solves the above problem using a penalty function approach and prove its convergence to the optimal solution. Our power control policy is applicable over any subset of links scheduled. To achieve high data rates over the links in addition to maximizing system utility, we schedule links using a degree-based greedy algorithm that limits multiaccess interference by scheduling a small number of transmissions around any scheduled receiver. The link scheduling algorithm and the power control algorithm are both amenable to distributed implementation in the framework of 802.11 LANs. Finally, we compare the performance of our joint scheduling and power control algorithms against CDMA using example utility functions and illustrate the superior performance of our algorithms.