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A Two Nutrient‐Response Function with Determination of Economic Optima for the Rate and Grade of Fertilizer for Alfalfa
Author(s) -
Pesek John,
Heady Earl O.
Publication year - 1956
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1956.03615995002000020025x
Subject(s) - fertilizer , mathematics , loam , nutrient , yield (engineering) , phosphorus , zoology , factorial experiment , statistics , potassium , agronomy , soil science , environmental science , soil water , chemistry , physics , organic chemistry , biology , thermodynamics
A replicated fractional factorial experiment with phosphorus and potassium fertilizer variables was conducted with alfalfa growing on Webster silty clay loam in 1952. Fertilizer was topdressed before growth was initiated in the spring, and the yields of hay determined from two cuttings. The range of fertilizer applications was wide enough to reach maximum yields. The data were analyzed and three different two‐variable equations were fitted to the observations. The equation which resulted in the best correlation with the observed data from this experiment was of the general form, Y = a + bK + cP + d K + e P + f KPwhere Y is the yield, and K and P the pounds of K 2 O and P 2 O 5 per acre respectively. The correlation coefficient was 0.8793 and significant at the 1% level. The last four coefficients of K and P were also significant at this level, while the first coefficient of K was significant at the 5% level. It was shown how this equation representing the response surface can be used to (1) determine the rates of P 2 O 5 and K 2 O combinations which resulted in the same yield levels; (2) calculate the least cost combination of the two nutrients for any given yield; (3) calculate the marginal yields of both nutrients; (4) determine the optimum level of application of each nutrient at constant levels of the other; and (5) calculate the optimum levels of both nutrients varying simultaneously. Finally, it was illustrated how the least cost combination, and rates of application of the two nutrients varied as different prices for fertilizer elements and hay were assumed under the conditions of this experiment.