Optimization of a two-dimensional nonlinear production-financial model of a
company is studied. With the use of the sufficient conditions of optimalit
y stated in the paper, on optimal policy of dividends and investments is fo
rmed as feedback controls. Part I is concerned with the construction of rou
tes, which are used in Part II for optimization in two classes of admissibl
e controls and generalization to problems under a constrained terminal stat
e of the company and nonlinear quality criterion.