Economic Study of Problems of Depletion of Several Interrelated Non-renewable Resources

In this paper we generalize the classic problem of the economic study of the extraction of non-renewable resources. The most notable generalizations presented here are the presence of constraints on the depletion rate, multiple resources and variable prices and costs over time. To solve the problem, we first use the theory of optimal control combined with a modification of the classic shooting method and an algorithm inspired by the cyclic coordinate descent algorithm. Numerous examples are presented to illustrate the possibilities the method offers.