The 1972 Club of Rome's report on the "Limits to Growth" predicted a gloomy future for the world and its resources, sparking an ongoing controversial debate. Essential aspects of the rise and decline scenario were increasing resource scarcity and pollution. The central question was whether the scarcity of natural resources such as fossil fuels would limit growth and cause a substantial decline in standard of living. The report has been subject to the utmost scrutiny by academics and journalists. Recent re-examinations lend credibility to some of the conclusions reached in the report. Following the publication of the report, a group of distinguished economists countered the scarcity argument in a series of papers now commonly referred to as the Dasgupta-Heal-Solow-Stiglitz (DHSS) model. Their efforts resulted in a substantial theoretical contribution to the theory of economic growth and a standard model with resource constraints. One argument was that man-made capital could substitute resources in the production of consumption goods. Despite an extensive theoretical investigation, a complete analysis of the model was only recently for constant returns to scale and in the absence of capital depreciation. We offer a complete analysis of the welfare-maximising capital investment and resource depletion policies in the DHSS model with capital depreciation and any returns to scale. We characterise the optimal policies by applying an appropriate version of the Pontryagin maximum principle for infinite-horizon optimal control problems, and discuss the welfare-maximising policies.