How do you minimize and maximize #f(x,y)=x-y/(x-y/(x-y))# constrained to #1<yx^2+xy^2<16#?

1 Answer
Cesareo R.
Feb 20, 2017

See below.

Explanation:

This problem can be successfully handled with the Lagrange Multipliers technique.

The local maxima/minima points are

#((f(x,y),x,y, "type"), (-0.750704,-1.71756,1.25284,"maximum"), (1.81974,0.562693,-1.64382,"minimum"), (-3.39363,-4.05723,2.44297,"maximum"), (3.33301,1.4188,-4.14166,"minimum"))#

Attached a plot showing the feasible region superimposed to the objective function level curves, with the local maxima/minima points.

enter image source here

Related questions
See all questions in Solving Optimization Problems
Impact of this question
1534 views around the world
You can reuse this answer
Creative Commons License