How Do You Solve Optimization Problems with Lagrange Multipliers?

[peace89]

Find the values of x, y and z that minimize the function f ( x, y , z)= x^2 + y^2 + z^2- 6x- 3y -z subject to the constraint 11-2x-y-z= 0

x=....

z=.....

f = ....

λ=.....

dont know what do do

thank you

 

[Sethric]

This problem is set up for Lagrange multiplier method. What does that stipulate?

 

[mege]

Remember your Lagrange multiplier method.

\nabla f(x,y,z) = \lambda \nabla g(x,y,z), g(x,y,z)=0