A carpenter has been asked to build an open box with a square base, where an open box means a box without a top. The sides of the box will cost $3 per square meter, and the base will cost $3 per square meter. What are the dimensions of the box of maximal volume that can be constructed for $36 ?

Find a functionf(x) for the volume of the box.

f(x)=?

Letx andzbe the dimensions that maximize the volume of the box.

x=?

z=?