The protected cultivation system provides vegetable crops with environmental conditions that suit their vegetative and fruitful growth in terms of temperatures and intensity of lighting. Inside the greenhouse, all environmental factors are controlled and modified to suit plant growth in order to reach the largest possible amount of yield, based on the agricultural development strategy until 2030, which It seeks to make the best use of limited resources, whether water or land, so protected agriculture comes at the forefront of the solutions, means and techniques necessary to confront this. The research also aims, through its estimation of production functions, to identify the most important production elements specific to the production of cucumbers, as well as to estimate the production elasticity for those elements and calculate the total specific elasticity. Measuring the optimal size and determining returns on capacity and economies of scale, the optimal production volume that minimizes costs for cucumber crop productivity for the third category in the study sample was about 12.5 tons, and that the average total production size of the greenhouse in the third category in the study sample amounted to about 11.7 tons, that is, less than the optimal production size. As for the volume of economic production that maximizes profit, it amounted to about 13.9 tons, and the elasticity of production costs was estimated at about 0.53, which indicates that the production of the cucumber crop in the third category in the study sample takes place in the stage of increasing return to capacity, because the elasticity of costs is a reflection of the elasticity of production, as the total production elasticity was estimated. By about 4.25, this shows that the percentage of increase in the quantity of the total output of the greenhouse is less than the percentage of increase in the quantity of production elements used, which means an increase in the return to capacity because the production elasticity is greater than the correct one.