# How do you maximize and minimize #f(x,y)=1/x+y^2+1/(xy)# constrained to #2<x/y<4#?

##### 1 Answer

Dec 23, 2016

See below.

#### Explanation:

Using the Lagrange multipliers technique we can find the local minima/maxima. For this problem there are four local minima at

Attached the feasible region plot showing the local minima. The black arrow show the objective function growing rate at each point.