This article investigates a resource allocation problem with a clear economic interpretation. The process dynamics is described in terms of a linear production function. An optimal solution of the control problem is constructed in analytical form. Equal and different positive depreciation rates are considered. The optimal solution is obtained by Pontryagin's maximum principle, which provides a methodologically interesting approach. An alternative approach based on a special representation of the functional is also considered. The reachability set is constructed assuming equal depreciation rates for the controlled plant. An explicit analytical expression is obtained for the optimal value of the functional in terms of the problem parameters. This expression is useful for future analysis.