kawsar
- 13
- 0
1. Use the method of Lagrange multipliers to nd the minimum value of
the function:
f(x,y,z) = xy + 2xz + 2yz
subject to the constraint xyz = 32.
I understand the method how Lagranges Multipliers is donw done but seem to have got stuck solving the Simultaneous Equations involving the Partial Derivatives involving \lambda.
I think the 3 Partial Derivatives (set equal to 0) are:
f_{x}=y+2z-\lambdayz=0
f_{y}=x+2z-\lambdaxz=0
f_{z}=2x+2y-\lambdaxy=0
Any chance helping me work out how I can solve x, y and z in terms of \lambda OR if I've made an earlier mistake somewhere, sorting that out for me?
Thanks
edit: f_{x} is supposed to be f sub x - Don't know how to write that with the editor.
the function:
f(x,y,z) = xy + 2xz + 2yz
subject to the constraint xyz = 32.
I understand the method how Lagranges Multipliers is donw done but seem to have got stuck solving the Simultaneous Equations involving the Partial Derivatives involving \lambda.
I think the 3 Partial Derivatives (set equal to 0) are:
f_{x}=y+2z-\lambdayz=0
f_{y}=x+2z-\lambdaxz=0
f_{z}=2x+2y-\lambdaxy=0
Any chance helping me work out how I can solve x, y and z in terms of \lambda OR if I've made an earlier mistake somewhere, sorting that out for me?
Thanks
edit: f_{x} is supposed to be f sub x - Don't know how to write that with the editor.