# More lagrange...

• Nov 30th 2009, 03:43 PM
seekay
More lagrange...
Hey

Find max/min

f(x,y,z) = xyz

constraints x+y+z=5
xy+yz+zx=7

So I let g(x,y,z) = x+y+z-5
h(x,y,z) = xy+yz+zx-7

Then let Delta_f=lamda*Delta_g + mu*Delta_h .... and g(..) = 0 & h(..) = 0

So the equations I got were:

yz = lamda + mu(y+z)
xz = lamda + mu(x+z)
xy = lamda + mu(x+y)
x+y+z=5
xy+yz+zx=7

With a bit of algebra, I got 3*lamda + 10*mu = 7

but I'm a bit lost with the rest of the algebra to get critical points for x,y,z ?

Anyone want to give it a shot? :]

thanks!
• Nov 30th 2009, 04:26 PM
Jester
Quote:

Originally Posted by seekay
Hey

Find max/min

f(x,y,z) = xyz

constraints x+y+z=5
xy+yz+zx=7

So I let g(x,y,z) = x+y+z-5
h(x,y,z) = xy+yz+zx-7

Then let Delta_f=lamda*Delta_g + mu*Delta_h .... and g(..) = 0 & h(..) = 0

So the equations I got were:

yz = lamda + mu(y+z)
xz = lamda + mu(x+z)
xy = lamda + mu(x+y)
x+y+z=5
xy+yz+zx=7

With a bit of algebra, I got 3*lamda + 10*mu = 7

but I'm a bit lost with the rest of the algebra to get critical points for x,y,z ?

Anyone want to give it a shot? :]

thanks!

Instead of adding the three equations and using the constraits as you have, try subtracting the equations in pairs and factoring and see where that gets you.