The aim of the research in the present paper is to find a mathematical relation between the agricultural yield and the dose of fertilizers, on the one hand; on the other hand, it attempts to give a theoretical and graphic method for benefit optimisation. It is common knowledge that the models used in mathematizing the agricultural yield in relation to the doses of chemical fertilizers with nitrogen, phosphorus and potassium applied on experimental fields are based on non-linear functions. Of these, the ones used most often are exponential functions with negative exponent. Such an example is the one that uses the Mitscherlich function, which is given by relation (1). In the present paper, the function that gives the relation between the agricultural yield, , and the doses of fertilizers, , is given by relation: , which is a function as good for the case as the ones mentioned above, but different from them in that it uses hyperbolic functions. The constants that are involved in the expression of the above-mentioned function are determined with the least squares method, by comparison with the experimental data. By graphic representation of both function (3) and the experimental data in Table 1, we get the graph in Figure 1. The graph shows good concordance between the theoretic curve and the experimental data. The optimal solution for the dose of fertilizers is obtained by annulling the derivative in the expression of the benefit, or, just as well, by the graphic method given in Figure 2. From the point of view of the practical applications, this paper gives a method for the optimisation of use of the fertilizers with nitrogen, phosphorus and potassium, combining theoretical method with graphic methods. The paper is of practical interest also because it studies the adequate proportions of the three active substances used in fertilizers ( ); these chemical components are never used in equal percentages, whichever the crop might be.

fertilization, Mitscherlich, least squares, modeling

Presentation: oral