Lagrange multipliers

  • Thread starter nhartung
  • Start date
  • #1
56
0

Homework Statement


Assume that the surface temperature distribution of an ellipsoid shaped object given by 4x2 + y2 + 4z2 = 16 is T(x,y,z) = 8x2 + 4yz - 16z + 600.


Homework Equations





The Attempt at a Solution


I'm assuming we just have to find the maximum value of this function using the lagrange method.

I started by writing the equation like this:

8x2 + 4yz -16z + 600 - 4x2[tex]\lambda[/tex] - y2[tex]\lambda[/tex] - 4z2[tex]\lambda[/tex] + 16[tex]\lambda[/tex].

Then I found the 4 partials and set them to 0:

fx = 16x - 8x[tex]\lambda[/tex] = 0
fy = 4z - 2y[tex]\lambda[/tex] = 0
fz = 4y - 16 - 8z[tex]\lambda[/tex] = 0
f[tex]\lambda[/tex] = -4x2 - y2 - 4z2 + 16 = 0

My problem comes next when I try to solve this system of equations.
When I solve them I get:
x = 1 (or 0?)
y = z = -(4/3)
[tex]\lambda[/tex] = 2

These don't check out.

Does it looks like I'm going about this problem correctly? If so what am I doing wrong when solving the system of equations?
 

Answers and Replies

  • #2
56
0
ah nevermind it checks if I use x = 0.
 

Related Threads on Lagrange multipliers

  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
8
Views
2K
Top