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# Thinking Outside the Box -- or Maybe Just About the Box

#### Introducing the Regular Slotted Container

It is our contention that there is a better box problem to be examined - a box problem that students will see as realistic as well as to be able to explore with tools from single-variable calculus. This adventure began a little over 25 years ago when one of the authors was curious about how to model realistic shipping boxes and tore one apart to find out. His first exploration was with a box known in the shipping industry as a Regular Slotted Container (RSC). The RSC is perhaps one of the most commonly utilized class of boxes in the shipping industry because it is one of the most economical boxes to manufacture and adapt for the shipment of most commodities. At first exploration, the construction of a RSC appears to require two variables but a simple but practical constraint makes it a problem appropriate for single variable calculus.

Let's first explain what exactly a RSC is. As shown below in figures 5 and 6, a Regular Slotted Container is constructed from a large rectangular sheet of corrugated cardboard. Depending on the construction details, it may be manufactured with a tab used to either glue or stitch the joint (the inclusion of the tab results in waste cardboard during production) or may rely on a taped joint making it a minimal shipping container (i.e. a box where there is ''no'' scrap corrugated cardboard generated in the manufacturing process). In either case, the lengthwise (normally outer) flaps meet at the center of the box allowing it to be affixed by tape or staples.

Figure 5: Construction schematics for the RSC (Safeway Packaging, n.d.)

 The box is closed Top flaps opened All flaps opened Completely disassembled

Figure 6. Various stages of a RSC being disassembled

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Meel, David and Thomas Hern, "Thinking Outside the Box -- or Maybe Just About the Box," Loci (August 2009), DOI: 10.4169/loci003321