The objective of this research is to minimize the weight of beverage cans subject to structural, geometric, manufacturing, and volume constraints. The structural constraints are: internal pressure, drop loading, and axial column loading which can buckle and damage the can. This study concentrates on the variation of the geometry of the can bottom. Parameterization is a key issue as three distinct parameter sets are essential to the optimization of the can: the Tooling parameters allow the can to be made, the geometric parameters allow the can to be analyzed by the finite element method, and the continuous parameters allow the can to be optimized. The optimization can be done only by integrating geometric, mechanical, mathematical, and physical insight to the problem. Finite element automation and monotonicity analysis were essential in optimizing this problem in a solution space with 14 variables. A sensitivity analysis of both the nominal and optimal design provided insight to the variation of tooling tolerances on the structural performance, fill volume, and weight of the can. Additional research could address robust design by minimizing sensitivity.