A company wants to design an open$-$top rectangular box with a square base that will hold a volume of $32$ cubic meters. The material for the base costs $$5$ per square meter, and the material for the sides costs $$3$ per square meter. What is the minimum cost of the box?

$$ $$180\mathrm{.}28$

$$168\mathrm{.}71$

$$170\mathrm{.}73$

$$159\mathrm{.}43$