A jewelry box is to made in the shape of a rectangular box with a square base. The volume of the box needs to be 250 cubic inches. The material used to manufacture the bottom side of the box costs $1 per square inch. The material for the four sides costs $2 per square inch and the material for the lid costs $7 per square inch. Find the dimensions that will minimize the cost of the material to manufacture the box.

Question

A jewelry box is to made in the shape of a rectangular box with a square base.  The volume of the box needs to be 250 cubic inches. The material used to manufacture the bottom side of the box costs $1 per square inch. The material for the four sides costs $2 per square inch and the material for the lid costs $7 per square inch. Find the dimensions that will minimize the cost of the material to manufacture the box.