Vol. 27, No. 3 Executive Publisher Solomon A
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The Journal UMAPPublisher COMAP, Inc. Vol. 27, No. 3 Executive Publisher Solomon A. Garfunkel ILAP Editor Chris Arney Associate Director, Mathematics Division Program Manager, Cooperative Systems Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Editor [email protected] Paul J. Campbell On Jargon Editor Campus Box 194 Yves Nievergelt Beloit College Department of Mathematics 700 College St. Eastern Washington University Beloit, WI 53511–5595 Cheney, WA 99004 [email protected] [email protected] Reviews Editor Associate Editors James M. Cargal Mathematics Dept. Don Adolphson Brigham Young University Troy University— Chris Arney Army Research Office Montgomery Campus Aaron Archer AT&T Shannon Research Laboratory 231 Montgomery St. Ron Barnes University of Houston—Downtown Montgomery, AL 36104 Arthur Benjamin Harvey Mudd College [email protected] Robert Bosch Oberlin College James M. Cargal Troy University— Montgomery Campus Chief Operating Officer Murray K. Clayton University of Wisconsin—Madison Laurie W. Arag´on Lisette De Pillis Harvey Mudd College James P. Fink Gettysburg College Production Manager Solomon A. Garfunkel COMAP, Inc. George W. Ward William B. Gearhart California State University, Fullerton William C. Giauque Brigham Young University Production Editor Richard Haberman Southern Methodist University Timothy McLean Jon Jacobsen Harvey Mudd College Walter Meyer Adelphi University Distribution Yves Nievergelt Eastern Washington University Kevin Darcy Michael O’Leary Towson University John Tomicek Catherine A. Roberts College of the Holy Cross John S. Robertson Georgia Military College Graphic Designer Philip D. Straffin Beloit College Daiva Kiliulis J.T. Sutcliffe St. Mark’s School, Dallas Subscription Rates for 2006 Calendar Year: Volume 27 Membership Plus Individuals subscribe to The UMAP Journal through COMAP’s Membership Plus. 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The UMAP Journal is published quarterly by the Consortium for Mathematics and Its Applications (COMAP), Inc., Suite 3B, 175 Middlesex Tpke., Bedford, MA, 01730, in cooperation with the American Mathematical Association of Two-Year Colleges (AMATYC), the Mathematical Association of America (MAA), the National Council of Teachers of Mathematics (NCTM), the American Statistical Association (ASA), the Society for Industrial and Applied Mathematics (SIAM), and The Institute for Operations Research and the Management Sciences (INFORMS). The Journal acquaints readers with a wide variety of professional applications of the mathematical sciences and provides a forum for the discussion of new directions in mathematical education (ISSN 0197-3622). Periodical rate postage paid at Boston, MA and at additional mailing offices. Send address changes to: [email protected] COMAP, Inc., Suite 3B, 175 Middlesex Tpke., Bedford, MA, 01730 © Copyright 2006 by COMAP, Inc. All rights reserved. Vol. 27, No. 3 2006 Table of Contents Editorial Because Math Matters Solomon A. Garfunkel ..................................185 About This Issue ........................................ 187 Special Section on the MCM Results of the 2006 Mathematical Contest in Modeling Frank Giordano . 189 Abstracts of the Outstanding Papers and the Fusaro Papers ...... 221 Sprinkler Systems for Dummies: Optimizing a Hand-Moved Sprinkler System Ben Dunham, Steffan Francischetti, and Kyle Nixon . 237 Fastidious Farmer Algorithms (FFA) Matthew A. Fischer, Brandon W. Levin, and Nikifor C. Bliznashki . 255 A Schedule for Lazy but Smart Ranchers Wang Cheng, Wen Ye, and Yu Yintao . ................. 269 Optimization of Irrigation Bryan J.W. Bell, Yaroslav Gelfand, and Simpson H. Wong ......285 Sprinkle, Sprinkle, Little Yard Bryan Camley, Bradley Klingenberg, and Pascal Getreuer ......295 Developing Improved Algorithms for Irrigation Systems Ying Yujie, Jin Qiwei, and Zhou Kai........................315 Judge's Commentary: The Outstanding Irrigation Papers Daniel Zwillinger .....................................329 Profit-Maximizing Allocation of Wheelchairs in a Multi-Concourse Airport Christopher Yetter, Neal Gupta, and Benjamin Conlee . .......333 Minimization of Cost for Transfer Escorts in an Airport Terminal Elaine Angelino, Shaun Fitzgibbons, and Alexander Glasser.....349 Application of Min-Flow to Airline Accessibility Services Dan Gulotta, Daniel Kane, and Andrew Spann . 367 Cost Minimization of Providing a Wheelchair Escort Service Matthew J. Pellicone, Michael R. Sasseville, and Igor Zhitninsky . 387 A Simulation-Driven Approach for a Cost-Efficient Airport Wheelchair Assistance Service Samuel F. Feng, Tobin G. Isaac, and Nan Xiao ...............399 Judges’ Commentary: The Fusaro Award Wheelchair Paper Daniel Zwillinger .....................................413 Publisher’s Editorial 185 Publisher’s Editorial Because Math Matters Solomon A. Garfunkel Executive Director COMAP, Inc. 175 Middlesex Turnpike, Suite 3B Bedford , MA 01730–1459 [email protected] The President has recently appointed a National Mathematics Advisory Panel. National newspapers carry lead editorials on math education. Why and why now? For many years, there has been a debate on how best to teach mathematics in our nation’s schools. There are a number of reasons why this discussion has gone on so long and become so heated. The first is that there is a great deal at stake. From Sputnik on, we have worried about our ability to compete in science and industry—first with Rus- sia, then with Japan, and now with India and China (not to mention Western Europe). And math matters. Mathematics is at the heart of technological in- novation, advances in engineering, physics, medicine, biology, and on and on. Mathematical models can forecast environmental change and monitor energy supply and demand. Without mathematics we wouldn’t have MRI’s or maps of the human genome. Second, we are not doing a very good job. U.S. students are falling behind students in most industrial countries as measured on any number of interna- tional tests. And again math matters. We know that the careers of the 21st century will require more and more quantitative reasoning. We know that in this global economy, companies can and will outsource jobs to countries with more mathematically skilled work forces. To quote CBS news great Fred Friendly, we don’t want to become a country “in which we take in each other’s laundry.” The third reason the debate is so heated is that it has become very political. We hear terms like “back to basics” and “fuzzy math.” But what’s lost in all of this is the kids. Education debates need at their heart to be about education. We want our children to learn, to understand and be able to use mathematics as they go through school and work. Not all students will go on to be mathematicians, but they will all be called upon to use the mathematics they know. The UMAP Journal 27 (3) (2006) 185–187. c Copyright 2006 by COMAP,Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP. 186 The UMAP Journal 27.3 (2006) I can’t emphasize this point strongly enough: The half-life of students in mathematics courses remains one year from 10th grade on. In other words, the number of students taking math in 11th grade is half those taking math in 10th, and so on for every year right up until the Ph.D. What happens to the other half? We simply cannot afford to throw away half of our students each year because they don’t have serious prospects of becoming research mathematicians. We can continue to ask students problems of the form: Solve for x in the equation x2 − 3x +1=0. Or we can ask at what proportion of performance enhancing drug use in the population is it cheaper