Finding in the model of gas fields the maximum length of their common "shelf"

A continuous aggregated dynamic model of the gas fields group is considered. The problem of maximizing the length of the common «shelf»of gas fields is posed and solved. The proposed problems belong to a class of optimal control problems with mixed constraints with nonfixed time and movable right end. The main mathematical apparatus is the Pontryagin maximum principle in Arrow form, which uses Lagrange multipliers. The obtained results are analyzed.