Volume 10 Part 2 Article 73: Graphic Optimization of Crop Production

Volume 10 Part 2 Article 73
Year 1979
Title: Graphic Optimization of Crop Production
Author: R.H. Kurtzman

Abstract:

The good businessman is constantly looking for ways to increase his profits. The scientist can often increase the value of his research by a more complete analysis of the relation between the quantity of a treatment and the quantity of the yield. Applied scientists may wish to show that the increase in yield from a proposed treatment, will in fact, give an increase in net profits, and what the economic optimum will be. Chanter (1974) suggested a way in which the mushroom grower -businessman or grower of some other crop might maximize his profits by a mathematical analysis of his operation. Those suggestions have value and should not be overlooked, but might be considered too complicated by most growers. Also, there are some dangers in using such an analysis; they will be discussed in this communication.

The data of Flegg, Jubb and Rothwell (1964) indicated that the effect of spawn “rate” on yield varied from one mushroom house to another. It is used in this communication only as an example. Chanter (1974) took the three data points from Flegg et al. (1964), and drew a curve from that data. Figure 1 shows three possible curves from that data. It is often said that one can easily find a curve to fit any three points on a graph. That is true whether there is any relationship between the numbers or not. The reason Chanter restricted his data to only three points was that his method depends on solving separate simultaneous equations for each point. As the number of points increases, the difficulty of the mathematics increases rapidly. Each additional point requires an additional pair of simultaneous equations for each of the preceding points. While three points require only three sets of simultaneous equations, five points require ten sets, and seven points require 21 sets of simultaneous equations! In the garphic method, described in this communication, each new point simply rtequires converting the data for that point into reciprocals.

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