Cooper Section $8\mathrm{.}13\backslash$#$18$

A wise old troll wants to make a small hut. Roofing material costs five dollars per square foot and wall materials cost three dollars per square foot. According to ancient troll customs the floor must be square, but the height is not restricted.

a$.$ Express the cost of the hut in terms of its height $\backslash ($ h $\backslash )$ and the length $\backslash ($ x $\backslash )$ of the side of the square floor.

Cost $\backslash (=\backslash$$ $\backslash )$

b$.$ If the troll has only $3375$ dollars to spend, what is the biggest volume hut he can build?

Largest volume $\backslash (=\backslash )$ cubic feet