A unified view of ostensibly disparate isoperimetric variational problems

A class of isoperimetric variational calculus problems is solved. It is shown that the said class ties together seemingly dissimilar optimal control problems in economics and physics, to wit, the classical nonrenewable resource extracting model of the firm, the model of the patient worker, and the principle of maximum entropy. In particular, it is shown that a certain family of wealth maximizing nonrenewable resource extracting firms extract at the rate that maximizes the entropy of extraction, and that patient intertemporal utility maximizing individuals do not procrastinate and maximize the entropy of leisure.