Optimal resource allocation program in a two-sector economic model with a Cobb-Douglas production function

We consider the resource allocation problem for a two-sector economic model with a two-factor Cobb-Douglas production function on a finite time horizon with a terminal functional. The problem is reduced to some canonical form by a scaling of the phase variables and time. We prove the optimality of the extremal solution constructed on the basis of the maximum principle. The solution of the boundary value problem of the maximum principle is constructed in closed form for three cases of location of the initial plant state.