Optimal applied water and nitrogen for corn

Water and fertilizer applications should be limited due to scarce resources and environmental protection aspects. An analysis of crop yield production and profit maximization was conducted to determine the optimal water and nitrogen allocation. In this analysis based on crop production and cost functions, a series of equations for determination of applied water and nitrogen for three conditions of maximum yield (wm and Nm, respectively), maximum profit under limited land (wl and Nl, respectively) and maximum profit under limited water (ww and Nw, respectively) were derived. The associated crop production function was determined from the results of a corn experiment with four levels of nitrogen fertilization and varying amounts of applied water via a line source of sprinkler irrigation. The previously derived equations were also applied to the experimental field data and finally the optimum amounts of applied water and nitrogen were determined at different conditions (wm, wl, and ww for water and Nm, Nl, and Nw for nitrogen, respectively). At present market value (15.55 Rls/m3 for water and 652 Rls/kg for nitrogen) the amounts of wm, wl, and ww were 1.0, 0.99, and 0.74 m, respectively, and the amounts of Nm, Nl, and Nw were 212, 212, and 206 kg N/ha, respectively. Because of the low price of nitrogen, the optimum amounts of nitrogen at three mentioned conditions were similar. But if the price of nitrogen and water are increased (i.e. 50000 Rls/kg N and 100 Rls/m3 water), then the amounts of applied nitrogen and water at the mentioned three conditions would be 212, 67, and 61 kg N/ha, and 1.00, 0.93, 0.84 m, respectively. When water is limiting, the optimum amount of applied water would not be different by changing the water price, however, it may be increased by a little amount when the nitrogen price is increased.