An open$-$top rectangular box is being constructed to hold a volume of $200i{n}^3.$ 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 $10$ cents$/i{n}^2.$

The remainder of the sides will cost $3$ cents $\frac{?}{i{n}^2}.$

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

Front width: in$.$

Depth:

Height:

in$.$