Increased competitiveness in the manufacturing industry demands optimizing performance at each level of an enterprise. Optimizing performance in terms of indicators such as manufacturing cost requires knowledge of cost-inducing variables from product design and manufacturing. However, the number of variables that affect manufacturing cost is very high and optimizing all variables is time intensive and computationally difficult. Thus, it is important to identify and optimize select few variables that have high potential for inducing cost. Towards that goal, a dimension reduction method combining dimensional analysis conceptual modelling framework and graph centrality theory is proposed. The proposed method integrates existing knowledge of the cost inducing variables, their interactions, and input-output relationship for different functions or behaviour of a system, in the form of a causal graph. Propagation of optimization objectives in the causal graph is checked to identify contradictory influences on the variables in the graph. Following the contradiction analysis, graph centrality theory is used to rank the different regions within the graph based on their relative importance to the optimization problem and to cluster the variables into two optimization groups namely, less important variables and most important variables relative to optimizing cost. The optimization problem is formulated to fix less important variables at their highest or lowest levels based on their interaction to cost and to optimize the more important variables to minimize cost. The proposed dimension reduction method is demonstrated for an optimization problem, to minimize the production cost of the bladder and key mechanism for a high-field superconducting magnet at CERN, capable of producing a 16 Tesla magnetic field. It was found that the graph region representing the electromagnetic force and resultant stress generated during energizing of the magnet ranked highest for influence on the bladder and key manufacturing cost. An optimization of the stress and its associated variables to minimize the manufacturing cost is performed using a genetic algorithm solver in Matlab.