Abstract
Depending on the production function, irrigation water cost function and the sale price of yield, previously, lengthy mathematical expressions have been developed to estimate the optimal levels of water used in deficit irrigation, that would maximize yield (Wm), under water limiting (Ww), and under land limiting (Wl) and the amount of water that leads to income equal to income of Wm when land is limited (Wel), and that leads to farm income equal to farm income of Wm when water is limited Wew . Therefore, in this paper, firstly the previous lengthy expressions for (Wel) and (Wew) were simplified. Secondly, simple expressions for both (Wel) and (Wew) were derived under presence of rainfall. Thirdly, very simple mathematical relations between (Wm & Wl) and (Wm & Ww) were derived in order to determine much easier expressions than those previously derived for Wel, and Wew respectively, with and without rainfall.
