Question

How do you minimize and maximize `f(x,y)=e^x/e^y-x^2y` constrained to `0<xy+y^2<1`?

Answer 1

A local minimum at `x=-0.9453,y=-0.6334`

Explanation:

Using the Lagrange multipliers technique.

The figure shows part of the feasible region including objetive function level curves. The vector represents the objective function gradient at the point. This minimum point is attained at the feasible region frontier.