College Algebra, NOT Calculus (derivatives). United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000 cubic inches. Initially, they would like to know the dimensions of such a box with the minimum surface area. They are considering creating the box with a reinforced bottom. The box would be made out of a cardboard material costing 1 cent per square inch to build the walls and top, however the bottom would be constructed with stronger material, costing 2 cents per square inch to build. How do the dimensions of the box having the minimum surface area compare to the dimensions of the reinforced box which costs the least?

Imagine you have been contracted to solve this problem. That….