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 function f(x) for the volume of the box.
f(x)=?
Let x and z be the dimensions that maximize the volume of the box.
x=?
z=?