An open rectangular box with a square base of side-length "x" is to be constructed out of two different materials. The base is made out of heavier material costing $25 per m2 , while the four sides are made out of lighter material costing $10 per m2 . Our goal is to create the cheapest possible box that has a volume of 10m3 . Find an equation for the total cost of the box in terms of only x. Show work along with a suitable diagram. Then determine the global minimum of this equation and state the optimal dimensions for this box.