Using Lagrange multipliers for the homework

asked 2014-07-14 22:12:00 -0600

Dylan
650 ●2 ●16 ●25

updated 2014-07-15 19:12:42 -0600

I'm slightly confused by a certain step I'm at in the homework. I have looked for extrema in the whole unrestricted function, and found them without much difficulty, but for finding the extrema of the "edges" of the constrained area, I'm not sure how to apply our technique. By setting $\nabla f = \lambda \nabla g$, I get the two equations we need, but the third "equation" is actually the inequality we were provided with as a constraint. Can we use this inequality to solve for $x$ and $y$, or is there another method that I'm missing?

answered 2014-07-15 05:22:00 -0600

Christina
807 ●18 ●35 https://sites.google.com/...

updated 2014-07-15 06:42:07 -0600

I haven't had complete success with this either and may be using the wrong idea, but the idea I got from the book is that if you have two constraints, you can set $\nabla f = \lambda \nabla g + \mu \nabla h$. This is from 14.8, p. 381.

Since the inequality gave the restricted region, I think we can just set it up as two equations, $h$ and $g$ to check along these functions. But here is where I stopped and planned to spend some more time today trying to solve this system of equations because it looks pretty crazy.

Hope someone will add more if I am not going about this right....

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Using Lagrange multipliers for the homework

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