## Abstract

The box problem is taken from Calculus 1, where a student is asked to maximize the volume of a box constructed from a rectangular piece of cardboard with squares removed at the corners. We are interested in what the width and length need to be in order to have at least a rational answer for the optimum height. In 2000, Cuoco used Eisenstein triples to find the dimensions. Hotchkiss expanded on Cuoco's work in 2002 and used an elliptical equation to find the dimensions needed for the box. This paper answers two open questions posed by Hotchkiss: proving that the smallest possible distinct dimensions that produce an integral solution are 5 and 8. Also the minimum distnct dimensions are examined in general.

## Faculty Sponsor

Christina Soderlund

## Recommended Citation

Predmore, Marissa
(2008)
"The Box Problem,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 9:
Iss.
1, Article 7.

Available at:
https://scholar.rose-hulman.edu/rhumj/vol9/iss1/7