We use the network utility maximization (NUM) framework to create an efficient and fair medium access control (MAC) protocol for wireless networks. By adjusting the parameters in the utility objective functions of NUM problems, we control the tradeoff between efficiency and fairness of radio resource allocation through a rigorous and systematic design. In this paper, we propose a scheduling-based MAC protocol. Since it provides an upper-bound on the achievable performance, it establishes the optimality benchmarks for comparison with other algorithms in related work.