||In the present work the isoperimetric problem of the Calculus of Variations was studied. In the first and second part, the motivation and exact formulation of this problem was discussed, followed by the assertion on the necessary condition for its solution (Theorem 1). The proof of this theorem was performed. In the third part, the concrete example of this problem was calculated. In the final section, the isoperimetric problem for mathematical analysis of the economic model- "`The Economics of Exhaustible Resources"' was used.