A Question of Carpeting

Spacely Sprockets
1 Sprocket Way
City of Commerce, CA 55057
September 17, 2001

Math 104 Students
Wheaton College
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).

Yours sincerely,
M. Cogswell
CEO Spacely Sprockets