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Due to varying wireless channel conditions, the IEEE 802.11 wireless local area network (WLAN) standard supports multiple modulation types to accommodate the tradeoff between data rate and bit error rate. In Heusse(2003), Rousseau, Berger-Sabbatel and Duda theoretically analyzed a performance anomaly when multi-rate stations with different modulation types exist in IEEE 802.11 WLANs. The performance anomaly is: the aggregate throughput of those stations transmitting at a higher data rate will dramatically degrade below the same level as that of those stations transmitting at a lower data rate. In this paper, we address the anomaly problem and formulate a nonlinear mixed integer programming problem to maximize the total aggregate throughput of all stations subject to that the channel occupancy times among the stations transmitting at different data rates are kept at a fairness ratio. With its aid, a single-hop WLAN can dynamically accommodate the resource access usage to maximize the system throughput in varying fading environments. We prove that the optimization problem is intractable and propose a heuristic solution based on a penalty function with gradient-based approach to solve it. We show the effectiveness of the approach via computational experiments and provide some useful guidelines to regulate the parameters needed for the approach.