In this paper, we analyze a neoclassical model of economic growth. Such models are widely used for the analysis of macroeconomic processes. One of the important elements of the growth model is a production function, which relates an output production to quantities of inputs (capital, labor, etc.). Considering the dynamic variant of the model, we use the nonlinear dynamized Cobb -- Douglas production function. The main economic objective of this work is to show how to effectively manage the consumption policy to maximize the final capital and the total consumption. We reduce this problem to a dynamic nonlinear problem of optimal control. Its solution is constructed by R. Gabasov's adaptive method. We construct the optimal control (consumption policy) in the class of piecewise-constant functions. Numerical experiments are carried out to prove the reliability and efficiency of the approach. A software package is developed in the MATLAB environment.