Satisfying the demand for higher data rate and ensuring the quality of service requirements are gaining more research interest. Investigating the problem of resource management for mobile systems is crucial in solving this issue. This paper aims at optimizing the down-link physical resources allocation in LTE-A multi cell systems. This constitutes the allocation of the physical resources to optimize the spectral and power eciency under dierent down-link frequency partition congurations. The allocation objective is to increase the mobile service providers return on investment by increasing revenues and decreasing operational costs, while maintaining the minimum quality of service (QoS) requirements. A new scheme employing a utility-based