- #1
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 [tex]\lambda[/tex].
I think the 3 Partial Derivatives (set equal to 0) are:
f[tex]_{x}[/tex]=y+2z-[tex]\lambda[/tex]yz=0
f[tex]_{y}[/tex]=x+2z-[tex]\lambda[/tex]xz=0
f[tex]_{z}[/tex]=2x+2y-[tex]\lambda[/tex]xy=0
Any chance helping me work out how I can solve x, y and z in terms of [tex]\lambda[/tex] OR if I've made an earlier mistake somewhere, sorting that out for me?
Thanks
edit: f[tex]_{x}[/tex] 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 [tex]\lambda[/tex].
I think the 3 Partial Derivatives (set equal to 0) are:
f[tex]_{x}[/tex]=y+2z-[tex]\lambda[/tex]yz=0
f[tex]_{y}[/tex]=x+2z-[tex]\lambda[/tex]xz=0
f[tex]_{z}[/tex]=2x+2y-[tex]\lambda[/tex]xy=0
Any chance helping me work out how I can solve x, y and z in terms of [tex]\lambda[/tex] OR if I've made an earlier mistake somewhere, sorting that out for me?
Thanks
edit: f[tex]_{x}[/tex] is supposed to be f sub x - Don't know how to write that with the editor.