The vintage model of economic growth is revisited from the point of view of viability compared with optimality. A viable state is a state from which there exists at least one trajectory in consumption, scrapping time, and investment which remains inside the set of constraints until a given time horizon, allowing the agent to maintain an adequate level of consumption throughout the period. There exists a largest set of viable states, including all others, called the viability kernel. This concept is an interesting addition to those of equilibria and optimal paths. The viability kernel shrinks with scrapping time as the technological rate increases, showing that machines must be renewed in line with this rate in order to maintain consumption. The viable and optimal solution in the sense of inter-temporal consumption is obtained on the viability boundary under an auxiliary system. Economic sustainability as defined by the Brundtland commission adds the restrictive criterion of non-decreasing social welfare. The viability kernel of sustainable solutions shows the necessity of limiting one’s consumption, by how much, and when. The viable, optimal, and sustainable solution is computed on the viability boundary under an auxiliary system that combines optimality and constraints.