Originally Posted by

**nameck** **1. The problem statement, all variables and given/known data**

Determine the dimensions of a rectangular box, open at the top, having volume

4 m3, and requiring the least amount of material for its construction. Use the

second partials test. (Hint: Take advantage of the symmetry of the problem.)

**2. Relevant equations**

**3. The attempt at a solution**

Volume, V= 4m^3

let x = length

y = width

z = height

4m^3 = xyz

x = 4/yz

because it is an open at the top rectangular box,

the Surface, S = 2xz + 2yz + xy

substitute x=4/yz inside the surface equation..

S = 8/y + 2yz + 4/z

to find the critical points, take the partial with respect to y and z.. the equal it to zero..

S'(y)= 2z - 8/y^2

S'(z)= 2y - 4/z^2

solve the equations, i get,

when y = 0, z = 0..

y = 8, z = 1/16

the problem is, what should i do next?