Re: maximization problem
- From: "Stephen J. Herschkorn" <sjherschko@xxxxxxxxxxxx>
- Date: Tue, 05 Jun 2007 21:58:38 -0400
chrizm7@xxxxxxxxx wrote:
Find the maximum of f(x1, ..., x_n) = (x1*x2*...*x_n)^2 subject to the
constraint
g(x1,...,x_n) = x1^2 + ... + x_n^2 = 1
I try to use lagrange multipliers. I take grad(f) and grad(g) and set
grad(f) = \lambda*grad(g)
but I always get stuck solving the nonlinear system of equations. Is
there a trick to doing this?
Letting y_i = (x_i)^2, your problem is
max sum(i=1..n, ln y_i)
s.t.
sum(i=1..n, y_i) = 1
y_i > 0 for all i
This should be easier to solve.
I suspect one could come up with some non-Lagrange argument that y_i = 1/n for all i should be the answer.
--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan
.
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