objective function

The quantity being optimized in a word problem, written as a function of the problem's variables.

Translating an optimization word problem starts by naming every quantity involved and writing the quantity being optimized as the objective function. When a paired constraint equation can be solved explicitly for one variable in terms of the other, substituting it into the objective collapses a two-variable problem back into an ordinary single-variable one, first- and second-derivative tests included.

Examples

For an open-top box of square base $x$ and height $h$ , the objective function is the volume $V=x^2h$ .