Geometric variability increases performance variability and degrades the mean performance of turbomachinery compressor blades. These detrimental effects can be reduced by using robust optimization to design the blade geometry or by imposing stricter manufacturing tolerances. This paper presents a novel computational framework for optimizing compressor blade manufacturing tolerances, and incorporates this framework into existing robust geometry design frameworks. Optimizations of an exit guide vane geometry are conducted. The single-point optimal geometry is found to depend on the manufacturing tolerances due to a switch in the dominant loss mechanism. Multi-point geometry optimization avoids this switch so that the geometry and tolerance optimization problems are decoupled.