Educational problem of explaining of the Maximum Principle

The Maximum Principle is a central result of the non-classical variational calculus, i.e., the optimization theory of control. The proof of the Maximum Principle is enough hard. And from educational point of view it is essential to give an easy version of the proof which explains the sense of the Maximum Principle and a clear idea of its proof. The Tent method worked out by the speaker gives such a clear idea that is very geometrical and visual. In the talk that idea would be explained.