Optimize x² + y² + z² - 2x subject to x² + y² + z² = 25

squenshl · Oct 12, 2009

Optimize f(x,y,z) = x² + y² + z² - 2x subject to the constraint g(x,y,z) = x² + y² + z² - 25 = 0

Step 1:
L = f - [tex]\lambda[/tex]g = x² + y² + z² - 2x - [tex]\lambda[/tex](x² + y² + z² - 25).

Step 2:
L_x = 2x - 2 - 2[tex]\lambda[/tex]x = 0
L_y = 2y - 2[tex]\lambda[/tex]y = 0
L_z = 2z - 2[tex]\lambda[/tex]z = 0

What do I do now? Please help.

Office_Shredder · Oct 13, 2009

I see four equations and four unknowns (don't forget that g(x,y,z)=0 gives you another equation!). Have you tried solving for those unknowns?

Optimize x² + y² + z² - 2x subject to x² + y² + z² = 25

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