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Quadratic Programming Method for Determining Optimum Nitrogen Rates for Winter Wheat During Tillering

Agro-Economic Div., Int. Fertilizer Develop. Ctr, Muscle Shoals, AL 35660

D. B. Taylor and M. M. Alley^*

Deps. of Agric. Econ. and Agronomy,, Virginia Polytechnic Inst. and State Univ.,, Blacksburg, VA 24061.

^* Corresponding author.

The objective of this study was to determine the recommended amount of N fertilizer to be applied to winter wheat (Triticum aestivum L.) at Zadoks growth stage (GS) 25 that would optimize the use of a model previously developed to predict N required at GS 30. Quadratic programming models were developed for six experimental sites in Virginia to maximize marginal profit with N fertilizer application. First, the models were solved to determine the amounts of N necessary at GS 25 and at GS 30 to produce maximum profit. Then, four N fertilizer rates at GS 25 (N25) (0, 30,60, and 100 kg N ha^–1) were evaluated by replacing the N25 value with each of these four predetermined amounts, and to again determine maximum profit. The difference (D) between the yields with maximum attainable profit (Y) without replacing N25 and the yields in which N25 was replaced With 0,30,60, and 100 kg N ha^–1 (Y^R) was then calculated (D = Y –Y^R). The best N25 recommendation was selected as the one that minimized the mean value and standard deviation of D. This method was used for three N fertilizer:wheat price ratios (2.0,4.0, and 8.0). The results indicated that the best recommendations for N25 were 50 to 60 kg N ha^–1 for N fertilizer:wheat price ratios of 2.0 and 4.0, and 40 to 50 kg N ha^–1 for a price ratio of 8.0.

Received for publication July 6, 1987.

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