Given a set of design and process parameters, today's design engineer is currently able to assess the quality and cost of the final product through numerical simulation. The parameters are used to create a finite element model of the manufacturing process and the ensuing analysis is performed to evaluate the process response. The engineer then studies the response to predict the ultimate quality of the product. Through some other means, the engineer also estimates the relative cost of the design versus other designs. At this point, the engineer entertains the following questions: (1) If the current design is not suitable, how do I improve it? (2) If the current design is suitable, how might I improve it, or reduce its cost? Presently, these questions are resolved by the engineer's experience and/or trial and error. Although a satisfactory design will ultimately be determined, there is no guarantee the chosen design is the most cost efficient, i.e. optimal. This research is to develop a systematic means to obtain optimally designed manufactured products, concentrating on the process of metal casting. The approach combines the finite element method, numerical optimization, and recent advances in explicit sensitivity analysis to investigate various means of quantifying the effects of varying casting parameters to obtain on optimal casting. Such a rational design method should allow the more efficient and accurate design of molds for casting, resulting in lower casting cost and higher quality.