A contour map for a function $ffis$ shown. Estimate the value $offy(3,19)fy(3,19)$

$An$ open$-$top rectangular box $is$ being constructed $to$ hold a volume $of250i{n}^3.$

The base $of$ the box $is$ made from a material costing $8$ 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:

$in.$