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We present a unified analytical framework that maximizes generalized utilities of a wireless network by network-wide opportunistic scheduling and power control. That is, base stations in the network jointly decide mobile stations to be served at the same time as the transmission powers of base stations are coordinated to mitigate the mutually interfering effect. Although the maximization at the first glance appears to be a mixed, twofold and nonlinear optimization requiring excessive computational complexity, we show that the maximization can be transformed into a pure binary optimization with much lower complexity. To be exact, it is proven that binary power control of base stations is necessary and sufficient for maximizing the network-wide utilities under a physical layer regime where the channel capacity is linear in the signal-to-interference-noise ratio. To further reduce the complexity of the problem, a distributed heuristic algorithm is proposed that performs much better than existing opportunistic algorithms. Through extensive simulations, it becomes clear that network-wide opportunistic scheduling and power control is most suitable for fairness-oriented networks and under loaded networks. We believe that our work will serve as a cornerstone for network-wide scheduling approaches from theoretical and practical standpoints.