Optimal resource distribution program in a two-sector economic model with a Cobb-Douglas production function with distinct amortization factors

We consider a resource distribution problem on a finite time interval with a terminal functional for a two-sector economic model with a two-factor Cobb-Douglas production function with distinct amortization factors. The problem can be reduced to a canonical form by scaling the state variables and time. We prove the optimality of an extremal solution constructed with the use of the maximum principle. For the case in which the initial state of the plant lies above the singular ray, the solution of the boundary value problem of the maximum principle is presented in closed form.