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This paper is concerned with the application of formal optimization methods to the design of mixed-granularity field-programmable gate arrays (FPGAs). In particular, we investigate the appropriate mix and floorplan of heterogeneous elements: multipliers, RAMs, and lookup table (LUT)-based logic, in order to maximize the performance of a set of digital signal processing (DSP) benchmark applications, given a fixed silicon budget. A mathematical programming framework is introduced, along with a set of heuristics, capable of providing upper-bounds on the achievable reconfigurable-to-fixed-logic performance ratio. Moreover, we use linear-programming bounding procedures from the operations research community to provide lower-bounds on the same quantity. Our results provide, for the first time, quantifications of the optimal performance/area-enhancing capability of multipliers and RAM blocks within a system context. The approach detailed provides a formal mechanism to explore future technology nodes.