An open$-$top rectangular box is being constructed to hold a volume of $350$ in$3.$ The base of the box is made from a material costing $7$ cents$/$in$2.$ The front of the box must be decorated, and will cost $9$ cents$/$in$2.$ The remainder of the sides will cost $3$ cents$/$in$2.$

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