I haven't done this for a long time so i'm bit stuck on this

Max. $\displaystyle V=xyz$ for $\displaystyle x,y,z \geq 0$ with constraints

$\displaystyle xy + yz + zx = 1$

$\displaystyle x + y + z = 3$

I found:

$\displaystyle h = xyz + \lambda(xy+yz+zx-1) + \mu(x+y+z-3) $

$\displaystyle \frac{\partial}{\partial x}=yz + \lambda(y+z) + \mu $

$\displaystyle \frac{\partial}{\partial y}=xz + \lambda(y+x) + \mu $

$\displaystyle \frac{\partial}{\partial z}=xy + \lambda(y+x) + \mu $

$\displaystyle \frac{\partial}{\partial \lambda}=xy +yz + zx -1 $

$\displaystyle \frac{\partial}{\partial \mu}=x + y + z -3 $

Think this is correct step up to this point, but when I try to rearrange above equation to find $\displaystyle \lambda and \mu$ I couldn't do it.

Please help me, thank you.