- Use the Arithmetic Mean -- Geometric Mean
Inequality to find the maximum volume of a box made from a 25
by 25 square sheet of cardboard by removing a small square from
each corner and folding up the sides to form a lidless box.

- Determine what shape boxes could be created
by this method from the 25 by 25 square sheet to hold a volume
of 200 cu. units. 400 cu units? 800 cu units?

- Generalize. Use the AM-GM Inequality to discuss
the maximum volume of a box formed from an
**n**X**n**square sheet of cardboard.

- Why will the AM-GM Inequality not be a useful
tool when the sheet of cardboard is 20 by 25?

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