where FN, FP, and FK are the respective
amounts of fertilizer applied; and P N , P P , and
P K are the respective prices of each fertilizer.
The optimal rate of fertilizer application to a
crop is that rate which produces the maximum
economic returns at the minimum cost, and
this can be derived from a nutrient response
curve. Different models for response curves
are in use, but linear response-plateau models
and curvilinear models (e.g., quadratic,
exponential, inverse hyperbolic) are the most
widely used. A typical example is a quadratic
response function of the following form: