Abstract

We present a fresh look at an age-old calculus problem, the box problem. The box problem is traditionally used as one of the typical exemplars for the study of optimization. However, this paper illustrates that another box problem, tied much closer to reality, can be used to investigate optimization. In particular, we present an improved box problem and its real-world context along with activities that blend hands-on and applet-based investigations with a strong dose of analysis that culminates in other possible extensions and investigations.

Table of Contents

• Introduction
• Background
  • Historical References
  • Introducing the Regular Slotted Container (RSC)
  • Movie of the construction of the RSC
  • Discussing Dundas's (1984) analysis
• The first Box problem
  • Introduction
  • The first Box problem applet
  • The first Box problem activity
• The second Box problem
  • Introduction
  • The second Box problem applet
  • The second Box problem activity
• Reflections and Extensions
• References

This article uses Java Sketchpad to embed Geometer's Sketchpad figures.  In order to view Java Sketchpad content, you will need to install the Java plug-in for your browser.  Readers interested in Java Sketchpad and its capabilities may wish to read our Developers Area article, "Quick Interactive Web Pages with Java Sketchpad," by Michael E. Mays.

Appendix: Student Module

(Condensed from the article for student and classroom exploration)

• Introduction and Table of Contents
• The first Box problem applet and activity
• The second Box problem applet and activity