How do you minimize and maximize $f (x, y) = \frac{x^{2}}{y} + \frac{y^{2}}{x}$ $f(x,y)=x^2/y+y^2/x$ constrained to $1 < y x^{2} + x y^{2} < 16$ $1<yx^2+xy^2<16$ ?

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Answer 1 · 2017-01-10T09:55:08

See below.

This problem can be solved using the so called Lagrange Multipliers.
The local minima/maxima can thus be located.

For this problem we have two points:

$((f(x,y),x,y),(4,2,2),(1.58,0.794,0.794))$

Attached a plot showing a piece of feasible region with the two points. Both are local minima points.

enter image source here

How do you minimize and maximize f(x,y)=x^2/y+y^2/xf(x,y)=x2y+y2xf(x,y)=x^2/y+y^2/x constrained to 1<yx^2+xy^2<161<yx2+xy2<161<yx^2+xy^2<16?