The importance of research is highlighted in seeking to increase the dunumah of yield, which leads to providing indicators for decision-makers in drawing agricultural policy and managing production resources in an efficient manner. The research problem is focused on the lack of knowledge of cucumber growers in the Kirkuk Governorate - Hawija district to know the optimal size of farms, which leads to a decline. Production on the one hand and high production costs on the other hand, and given that Iraq is one of the developing countries, it suffers from many production obstacles, including the high elements of economic resources such as seeds, fertilizers, control materials and pesticides or importing them from outside the country, and based on the research problem, it aimed to: estimate the optimal volumes For areas and production of the option crop in the research sample, estimating the proportion of economies of scale achieved for the crop farmers by calculating the elasticity of the average cost function and the function coefficient. The optimum sizes of areas and production for the cucumber crop in Hawija district were extracted by drip irrigation method through the cost functions in the long run and the cost flexibility and function factor of the cucumber yield were extracted in the research sample. )15,517( tons, and the optimum areas of this crop reached (13,453) dunums, so the farmers of the cucumber crop by drip irrigation method do not achieve the optimum volume of production, and this means that there is a deviation from the optimal size of the yield of the research sample and in light of the results reached, the study recommended the adoption of The experiences of the owners of efficient farms and benefiting from them in employing their expertise in inefficient farms in order to reach full levels of efficiency, the need to activate the role of the agricultural extension apparatus in training and directing farmers to adopt modern techniques in irrigation.