A note on the heavy longest reach cantilever: an unconventional optimization problem

We analyze the problem of finding the shape of a heavy cantilever that minimizes volume and satisfies certain condition at the free end that corresponds to the so-called longest reach problem. The Pontryagin's maximum principle with cross-sectional area as "control" is used in the optimization procedure. We point out some specific properties of the problem. Namely, in one formulation we are faced with standard optimization problem and in another case with unconventional optimization problem.