For very simple problems, say that a function of two variables subject to a single equality constraint, it is most practical to apply the method of substitution.<ref>{{cite book |first=Mike |last=Prosser |title=Basic Mathematics for Economists |___location=New York |publisher=Routledge |year=1993 |isbn=0-415-08424-5 |chapter=Constrained Optimization by Substitution |pages=338–346 }}</ref> The idea is to substitute the constraint into the objective function to create a [[Function composition|composite function]] that incorporates the effect of the constraint. For example, assume the objective is to maximize <math>f(x,y) = x \cdot y</math> subject to <math>x + y = 10</math>. The constraint implies <math>y = 10 - x</math>, which can be substituted into the objective function to create <math>p(x) = x (10 - x) = 10x - x^{2}</math>. The first-order necessary condition gives <math>\frac{\partial p}{\partial x} = 10 - 2x = 0</math>, which can be solved for <math>x=5</math> and, consequently, <math>y = 10 - 5 = 5</math>.
