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?
1 Answer
Feb 24, 2015
Let's begin by putting in some definitions.
If we call
Now for the surfaces (=material)
Top&bottom:
Short sides:
Long sides:
Total area:
Substituting for
To find the minimum, we differentiate and set
Which leads to
Answer :
Short side is
Long side is
Height is
Check your answer!