RESPONSE SURFACES*


What They Are

 A response surface is a representation of the natural
relationship which exists between the quantity of a
product and various levels of one or more inputs used to
produce that product. That is, a response surface is an
estimate of the response of a product to different
quantities of one or more inputs utilized in the
production process. This representation can be physical,
tabular, graphic, or mathematical. A true response
surface with three dimensions (width, depth, and height)
results in graphic form when only two inputs are used to
obtain one product. In this form, the surface is similar
to a hill with quantities of the two inputs measured
toward the north and east and quantity of product
represented by height, or altitude. Each point on the
surface represents a combination of different quantities
of input A, input B, and yield of the product. In the
simplest case of only one input, the "surface" is a
straight line or a curve. In a more complex case with
three or more inputs used to produce one product, it is
impossible to imagine or draw the response "surface," so
it must be represented in mathematical form.
 The graphic or mathematical form of a response
surface is an artificial estimate of a real phenomenon
that exists in nature. The surface can represent the
response of a product to a continuous input, such as a
crop to fertilizer or animals to feed, etc. Because the
response is a natural biological phenomenon, it is not
constant for a fixed level of inputs. Rather, it is
subjected to a random variance. The granhic or
mathematical response surface represents the central
tendency of the response in terms of magnitude (level) and
of form (curvature).

Representative Forms

 To demonstrate the forms which response surfaces can
take, a two-dimensional case will be used with one input

*Much of this section was translated and adapted from
Hildebrand (1972).