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.


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

#( (f(x,y), x, y), (0.784703,-1.49595,-0.747977), (1.98053,1.84942,0.92471), (0.629311,-2.56756,-0.641891), (1.3392,3.0675,0.766876) )#

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

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