The paper considers a Cobb-Douglas function with n random elasticities. A theorem on the concavity and strict concavity of such a function is proved.

The article considers some optimization models with a nonlinear objective function and constraints in the form of equalities and inequalities. The model is considered in two forms – deterministic and stochastic, which allows it to be used to solve various optimization problems in physical and technical systems. The presented stochastic model is based on the inclusion of stochastic parameters into the well-known Cobb-Douglas function. The influence of stochastic variables on the optimal value of the objective function, depending on their distribution type, is analyzed.