The Box Problem
- 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?
Return to the EMAT 4600/6600