A steel box without a lid having volume 60 cubic feet is to be made from material that costs $4 per square foot for the bottom and $1 per square foot for the sides. Welding the sides to the bottom costs $3 per linear foot and welding the sides together costs $1 per linear foot. Find the dimensions of the box that has minimum cost and find the minimum cost. Use symmetry to obtain one equation in one unknown and use a CAS or Newton's Method to approximate the solution.