Recent studies have focused on the problem of resource allocation in systems in which multiple applications contend for multiple resources in order to satisfy their application level requirements. Q-RAM  assumes a system with multiple concurrent applications, each of which can operate at different levels of quality based on the system resources available to it. The goal of the model is to be able to allocate resources to the various applications such that the overall system utility is maximized under the constraint that each application can meet its minimum needs. However, Kuhn-Tucker optimality conditions are not satisfied at the result of the Q-RAM approach, which is based on Kuhn-Tucker conditions . In this work Q-RAM approach is modified and a new algorithm is proposed. Results of the Modified Q-RAM algorithm (MQ-RAM) satisfy the Kuhn-Tucker optimality conditions. The performance of the MQ-RAM algorithm is compared with that of Zoutendijk algorithm . A simplified radar optimization problem is solved by proposed optimization approach.