Some optimization problems with calculus

Arkady Kitover, Mehmet Orhon

Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average but motivated student of Calculus how to start from an inconspicuous textbook problem and to arrive at considerably more interesting and complicated problems, some of which can be subjects of independent research.