Abstract
Due to limited water resources and occurrence of recent droughts, the use of new management and planning methods for optimal irrigation scheduling of agricultural crops is inevitable. Present of appropriate mathematical and dynamic relationship between yield, evapotranspiration and water use efficiency parameters is the first and most important step in the optimal management of irrigation and application of deficit irrigation strategy in the field level. Accordingly, In order to determine the water Production function of Basil plant, a pot experiment was conducted in completely randomized block design with four irrigation treatments include: 100, 80, 60 and 40 percent of water requirements and three replications in the glass greenhouse of Kurdistan University. The results showed, in linear water production function, marginal water use efficiency for evapotranspiration values is fixed. So , It is not suitable for explanation details of relations. however in the quadratic water production function of marginal water use efficiency decreased while the increasing of evapotranspiration. And in The evapotranspiration of 348 mm was cut water use efficiency curv. At in this point elasticity of water production is 1, and it has maximum water use efficiency. The results showed the Maximum yield occurs at 376 mm evapotranspiration. At in this point elasticity of water production is 0. Observed maximum water use efficiency and maximum yield don’t happen at a same point ET would need 8 percent greater than the ET for maximum water use efficiency, while the value of yeild increased by 4/2 percent. In addition to that, Yeild Response factor in the quadratic water production function is greater than this factor in the linear production function

Keywords: Basil, Production function, Water use efficiency, Marginal analysis