An open$-$top rectangular box is being constructed to hold a volume of $200$ in ${?}^3.$ The base of the box is made from a material costing $7$ cents $\frac{?}{i{n}^2}.$ The front of the box must be decorated, and will cost $10$ cents $\frac{?}{i{n}^2}?$ The remainder of the sides witt cost $4$ cents $\frac{?}{i{n}^2}.$

Find the dimensions that will minimize the cost of constructing this box. Please show your anowers to at least $4$ decimal places.

Front width: $$ in$.$

Depth: $55\mathrm{.}0000$ in$.$

Height: $$ in$.$