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!