A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $5 per square foot and the...

A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $5 per square foot and the metal for the sides costs $10 per square foot. Find the dimensions that minimize cost if the box has a volume of 50 cubic feet.