- #1
smashyash
- 28
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Homework Statement
Find the minimum of f(x,y) = x^2 + y^2 subject to the constraint g(x,y) = xy-3 = 0
Homework Equations
delF = lambda * delG
The Attempt at a Solution
Okay, after lecture, reviewing the chapter and looking at some online information, this is what I have so far:
(using l for lambda)
x^2 + y^2 -(l)(xy-3)
x^2 + y^2-xyl-3l
find critical points:
Fx = 2x-ly = 0 --> 2x = ly --> x = ly/2
Fy = 2y-lx = 0 --> 2y = lx --> y = lx/2
Fl = -xy-3 = 0
so then substituting x and y values into the Fl equation,
(ly/2)(lx/2) - 3 = 0
so in all the examples I've seen, there's never an x or y in this equation, it should all be in terms of lambda. So what do I do know? I'm stuck!