Saddle point and optimum levels of nutrients in fertilizer trials

Abstract

When the response surface has a saddle point instead of a point of maximum, it is of great importance, from the practical viewpoint, to obtain alternative solutions for the optimum levels, i.e., the combination of dosis that gives the maximum yield. Three alternative solutions were studied by simulation: the point of absolute maximum (frontier point of maximum) in the experimental region, the experimental point of maximum, and the saddle point. Except the saddle point, the solutions presented good properties as the substitutes of the optimum levels. By using the criterion of frequency of maxima, a comparison was also made among nine treatment designs with three factors and 3, 5, 7 and 9 levels. The best treatment design was me 3³ factorial with equally spaced levels.