Abstract The latest achievements in science and technology lead to the development of new and more productive capital that can essentially increase a company’s profit. On the other hand, companies should invest not only in the productive capital, but also in science and technology. The optimal control of an economic system that divides its output among the production of consumption goods, the accumulation of new capital, and the contribution to science and technology is considered. The model is expressed as nonlinear integral equations with unknowns in the integrands and lower limits of integration. An optimization problem for the profit maximization is suggested. The necessary condition for an extremum and the second variation of the functional are derived. The structure of optimal solutions is analyzed. Interpretation of all results is provided.