The numerical techniques used in conventional optimization may not work for engineering design problems, which often present peculiar difficulties. Monotonicity analysis can identify a global optimum without any special computations and also prevent acceptance of false solutions generated by the numerical techniques. In the present paper, these advantages are demonstrated in a problem taken from the literature, for which diverse numerical solutions have been obtained. Monotonicity analysis identifies and proves the global optimum. Its application may require some algebraic rearrangement of the problem statement.