Introduction
Production agronomists routinely develop and use yield response curves to determine optimum management recommendations. Yield response analysis using two independent variables is obviously more complex than yield response analysis with one independent variable. The process of defining accurately an input - output relationship, a yield response curve for two independent inputs, requires that an experiment be established with 3 or more than 3 different levels of the two inputs. 3 levels of each of two inputs will result in 9 treatments per replication (1x1, 1x2, 1x3, 2x1, 2x2, 2x3, 3x1, 3x2, and 3x3). A minimum of at least 3 replications will also be desired, which results in a minimum of at least 27 plots. We cannot over emphasize the idea that it is difficult to develop an acceptable yield response curve. However, after a curve has been developed and determined by the investigator to be acceptable, finding the point of maximum economic return, is a trivial mathematical problem. This paper provides a cookbook approach that most people can easily follow to find points of maximum economic return given 1. an accepted yield response curve (yield = f(plant population, nitrogen applied), 2. the cost of seed, 3. the cost of nitrogen, and 4. the value of the produced corn.

Carlson’s side note: Understanding yield response is difficult. Over the years I have taught yield response theory to agronomy major, college seniors. There have been two distinct responses that I have encountered from students. The first which comes from the majority of students is “why are you wasting my time with the discussion of complex theory that I don’t need. I will be happy to use the expert’s recommendation”. The second response has come from some of my most capable students. It can best be described as anger at our educational system. The words I hear from this second group are something like this. “Why has this most significant decision making process been kept a secret from me? Why have I not been taught this long before the last semester of their senior year in college?” It is my hope that those of you reading this discussion that fit into this first group realize that there are those that are in the second group!!!!!

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