William B. Gearhart received his BS degree in engineering physics
and his PhD in applied mathematics from Cornell University. He
is currently a professor of mathematics at California State University, Fullerton. His research interests include approximation theory, numerical analysis, optimization theory, and mathematical modeling.
E-mail: wgearhart@fullerton.edu

Harris S. Shultz, professor of mathematics at California State
University, Fullerton, received his BA degree in mathematics from
Cornell University and his PhD in mathematics from Purdue University. He has directed numerous institutes for secondary mathematics teachers and been a frequent contributer to The AMATYC Review.
E-mail: hshultz@ fullerton.edu

In a well-known calculus problem, an open top box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. The task is to find the dimensions of the box of maximum volume. Typically, the length of the sides of the corners that produces the largest volume turns out to be an irrational number. However, there are examples of non-square rectangles for which this length is a rational number. In this article we show how to generate all cases in which integer values for the dimensions of the rectangle produce rational answers. This provides calculus instructors with several rectangles for which the optimal box has “nice” dimensions.