Question

How do you minimize and maximize `f(x,y)=x/e^(x-y)+y` constrained to `1<x^2/y+y^2/x<9`?

Answer 1

See below.

Explanation:

The attached plot shows the location of stationary points. The arrows represent the gradient of the objective function (black) and the boundary (red) at each stationary point. The feasible region in blue shows also level curves from the objective function. Those results were obtained using the Lagrange Multipliers technique.