A Question of Carpeting
1 Sprocket Way
City of Commerce, CA 55057
September 17, 2001
Math 104 Students
Norton, MA 02766
Dear Calculus Students:
I recently became CEO of Spacely Sprockets after a
somewhat messy hostile take-over, and I do not yet
trust anyone at the company to help me
with the critical decisions that will affect the success
of the corporation. When I went looking for help,
your enterprising and resourceful professor naturally
referred me to you.
I am remodeling my (nearly) oval office and replacing the
horrid orange carpeting left by my predecessor.
With the Board and shareholders
watching my every move, I want to be careful not to appear
profligate. I have already decided on a tasteful aqua shag, but
the carpeting comes on rolls in three different widths:
2.5 yards wide, 1.5 yards wide, and 1 yard wide.
I will use the same width for the entire office, but I'm not sure
which one to choose.
For each of the three widths, I need an analysis of how many square feet of
carpeting I must buy and an estimate of the amount of carpeting
that will be trimmed and wasted.
I also have the option to special order the carpeting in any width.
To impress the board with my thoroughness and all-around competence,
I would like to know what width I should order so that no more than
15 square feet of carpeting are wasted.
I am including a sketch of my office, and
I would appreciate an answer by October 1 since I need my office
to be ready for an important meeting later in the month with AOL-Time-Warner to discuss the
launching of the Sprockets Channel (``All Sprockets. All The Time''TM).
CEO Spacely Sprockets