What are the dimensions of a box that will use the minimum amount of materials, if the firm needs a closed box in which the bottom is in the shape of a rectangle, where the length being twice as long as the width and the box must hold 9000 cubic inches of material?
Let's begin by putting in some definitions.
If we call
Now for the surfaces (=material)
To find the minimum, we differentiate and set
Which leads to
Short side is
Long side is
Check your answer!