A three-dimensional, single-phase, multicomponent mathematical model is used for the analysis of a liquid-fed direct methanol fuel cell. Liquid phase is considered on the anode side, and gas phase is considered on the cathode side. The electrochemical kinetics, continuity, momentum, and species transport for methanol, water, and oxygen are all coupled to solve for different optimization scenarios. The effect of methanol crossover due to diffusion and electro-osmotic drag is incorporated into the model. A finite-volume-based computational fluid dynamics (CFD) code is used for the analysis and simulation of the performance of the fuel cell. The analysis model is coupled with the genetic algorithm and sequential quadratic programming optimization technique in seeking the global optimum solution of the fuel cell. Three optimization problems are considered. In the first problem, the maximization of the power density of the fuel cell with lower and upper bounds on the design variables is considered. The second problem considers the maximization of the power density with a constraint on the minimum allowable operating voltage as well as lower and upper bounds on the design variables. In the third problem, the minimization of the cost of the fuel cell is considered with constraints on the minimum allowable operating voltage and the minimum permissible power density as well as lower and upper bounds on the design variables. The performance characteristics of the optimum fuel cell, in the form of graphs of polarization (voltage versus current density), power density versus current density, power density versus voltage, methanol crossover versus current density, and methanol crossover versus voltage are presented and explained to help designers better understand the significance of the optimization results.