$An$ open$-$top rectangular box $is$ being constructed $to$ hold a volume $of300i{n}^3.$ The base $of$ the

box $is$ made from a material costing $5$ cents $\frac{?}{i{n}^2}.$ The front $of$ the box must $be$ decorated, and

will cost $12$ cents $\frac{?}{i{n}^2}.$ The remainder $of$ the sides will cost $2$ cents $\frac{?}{i{n}^2}.$

Find the dimensions that will minimize the cost $of$ constructing this box.

Front width:

$in.$

Depth:

$in.$

Height: