Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64 cm2

The problem is to optimize (find the maximum The problem is to maximiz the function 

f(x,y,z)=xyz 
With the constrain 
2(xy + xz + yz)=64; xy+xz+yz=32 
Using the Lagrange Multipliers 
F(x,y,z) = xyz - £(xy+xz +yz-32) 
Deriving with respect to x: 
yz - £(y+z)=0 ....i
Deriving with respect to y: 
xz - £(x+z)=0 ...ii
Deriving with respect to z: 
xy - 2£(x+y)=0 ....iii
Deriving with respect to £: 
xy+xz+yz=32 .....iv
From (i) and (ii) 
yz/2(y+z) = xz/2(x+z) 
y/(y+z) = x/(x+z) 
yx+yz=xy+xz 
y=x 
From (i) and (iii) 
x=z 
So, from (iv) 
x^2+x^2+x^2=32 
x^2=32/3 
x=y=z=sqrt (32/3) 
Vmax = sqrt (32/3)^3