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Various multimedia applications will be supported by beyond third generation (B3G) mobile communication systems. Mobile users may choose to simultaneously launch various applications with quality of service (QoS) constraints. Subject to the chosen applications' respective QoS constraints, the user may have to allocate her/his available resources for satisfaction maximization. In this paper, a utility-based algorithm is proposed to jointly allocate available power and uplink bandwidth, at mobile station (MS) level. Using Karush-Kuhn-Tucker (KKT) conditions and simulation, the algorithm is proved to be optimal. Under certain conditions, the algorithm (which may be applied in both downlink and uplink) is iterative and its convergence is shown by simulation.