Mathematical model applied to fertigation

Abstract

The objective of this work was to develop a mathematical model to assist farms in the determination of an optimal mixture of fertilizers in order to minimize the cost of nutritive solutions. This way, we developed a methodology that allows to identify an optimal mixture of fertilizers capable to assist farms in the management of fertigation. The methodology consisted of the development of an optimization mathematical model to assist in the determination of the optimal amount of fertilizers to be insert in the mixture in order to meet the nutritional needs of the crop at a minimum cost. In order to assist the user of this model, a mobile application was developed. Thus, this mobile application is a decision support tool to farms. Among the nonlinear programming methods, we opted for the Nonlinear Conjugate Gradient Method, this method is a particular case of the Conjugate Gradient Method, proposed to provide solutions of nonlinear problems. The proposed mathematical model complied with the restrictions recommended in fertigation regarding the calculation of the amount of fertilizer at a low cost; making it more efficient and complete. Therefore, the proposed methodology and the developed mobile application are important and accessible tools that could assist farms in the management of fertigation.