One of the most effective ways to think about an optimization is to visualize how a system’s response changes when we increase or decrease the levels of one or more of its factors. We call a plot of the system’s response as a function of factor levels a response surface.

The simplest response surface has a single factor, which we represent graphically in two dimensions by placing the response on the *y*-axis and the factor’s levels on the *x*-axis. The calibration curve below is an example of a one-factor response surface, which is represented by the equation

*A* = 0.008 + 0.00896*C*_{A}

where *A *is the absorbance and *C*_{A} is the analyte’s concentration in ppm.

For a two-factor system, the response surface is a plane in three dimensions in which we place the response on the *z*-axis and the factor levels on the *x*-axis and the *y*-axis. In the illustration below, (a) shows a pseudo-three dimensional wireframe plot for a system obeying the equation

*R* = 3.0 – 0.3*A* + 0.020*AB*

where *R *is the response, and *A *and *B *are the factors.

We can also represent a two-factor response surface using the two-dimensional level plot in (b), which uses a color gradient to show the response on a two-dimensional grid, or using the two-dimensional contour plot in (c), which uses contour lines to display the response surface.