Hierarchical scheduling of periodic resources has been increasingly applied to a wide variety of real-time systems due to its ability to accommodate various applications on a single system through strong temporal isolation. This leads to the question of how one can optimize over the resource parameters while satisfying the timing requirements of real-time applications. A great deal of research has been devoted to deriving the analytic model for the bounds on the design parameter of a single resource as well as its optimization. The optimization for multiple periodic resources, however, requires a holistic approach due to the conflicting requirements of the limited computational capacity of a system among resources. Thus, this paper addresses a holistic optimization of multiple periodic resources with regard to minimum system utilization. We extend the existing analysis of a single resource in order for the variable interferences among resources to be captured in the resource bound, and then solve the problem with Geometric Programming (GP). The experimental results show that the proposed method can find a solution very close to the one optimized via an exhaustive search and that it can explore more solutions than a known heuristic method.