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A piece of string $72$ cm long is to be used to tie up a small "rectangular" parcel. The string must pass twice around the width of the parcel and once around the length. What is the largest volume ($cm^3$) that the parcel can have? Disregard the insignificant amount of string used to tie the knot.

This is a question in a grade $7$ and $8$ math contest. Obviously, there is no calculus involved. How can we solve this?

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    To those putting this on hold: I'd say it is clear enough that the intention is to tie up a parallelepipedic package by going around it in all 3 "natural" directions, as in the following image: http://media.istockphoto.com/photos/paper-parcel-tied-with-twine-picture-id508101330 – 2017-02-28

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