This paper begins by formulating a finite horizon linear programming model for economic development. The formulation allows for heterogeneous capital goods and for nonnegativity constraints upon investment in each sector. It is then proved that a certain set of conditions are sufficient to ensure that an optimal solution to this T period, finite horizon plan will also coincide with an optimal solution during the first T periods of an infinite horizon plan. Among the restrictive conditions imposed to prove this sufficiency theorem are the following: gradualist consumption paths, no primary factors that cannot themselves be produced within the economy, a Leontief technology, and a characterization of the optimal finite horizon solution as one in which the terminal investment and output levels are positive. An illustrative numerical example is provided.