Answer
cube with edge length: $\dfrac{c}{12}$
Work Step by Step
Use Lagrange Multipliers Method:
$\nabla f=\lambda \nabla g$
Volume of a box is given by $V(f)=xyz$
$g=4x+4y+4z=c$
This yields $\lt yz,xz,xy \gt =\lambda \lt 4,4,4 \gt$
and $y=x,z=x$
Using the constraint condition we get, $4x+4y+4z=c \implies x=\dfrac{c}{12}$
Hence,
the box is a cube with edge length: $\dfrac{c}{12}$
