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Vol. 3, No On Jargon Editor Reviews Editor Chief Operating Officer Copy Editor Julia Collins

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Vol. 3, No On Jargon Editor Reviews Editor Chief Operating Officer Copy Editor Julia Collins
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  The UMAP Journal Publisher COMAP, Inc.  Vol. 3  , No   Executive Publisher Solomon A. Garfunkel ILAP Editor Chris ArneyDept. of Math’l SciencesU.S. Military AcademyWest Point, NY 10996 david.arney@usma.edu On Jargon Editor Yves NievergeltDept. of MathematicsEastern Washington Univ.Cheney, WA 99004 ynievergelt@ewu.edu Reviews Editor  James M. CargalMathematics Dept.Troy University—Montgomery Campus231 Montgomery St.Montgomery, AL 36104 jmcargal@sprintmail.com Chief Operating Of fi cer Laurie W. Arag´on Production Manager George Ward Copy Editor  Julia Collins Distribution  John Tomicek  Editor Paul J. CampbellBeloit College700 College St.Beloit, WI 53511–5595 campbell@beloit.edu Associate Editors Don Adolphson    Ron BarnesArthur BenjaminRobert Bosch James M. CargalMurray K. ClaytonLisette De Pillis James P. Fink Solomon A. GarfunkelWilliam B. GearhartWilliam C. GiauqueRichard Haberman Jon JacobsenWalter MeyerYves NievergeltMichael O’LearyCatherine A. Roberts John S. RobertsonPhilip D. Straf  fi n J.T. Sutcliffe       ••    U. of Houston—DowntnHarvey Mudd CollegeOberlin CollegeTroy U.— MontgomeryU. of Wisc.—MadisonHarvey Mudd CollegeGettysburg CollegeCOMAP, Inc.Calif. State U., FullertonBrigham Young Univ.Southern Methodist U.Harvey Mudd CollegeAdelphi UniversityEastern Washington U.Towson UniversityCollege of the Holy CrossGeorgia Military CollegeBeloit CollegeSt. Mark’s School, Dallas  Subscription Rates for 201 1  Calendar Year: Volume 3 2 Institutional Web Membership (Web Only) Institutional Web Memberships do not provide print materials. Web memberships allowmembers to search our online catalog, download COMAP print materials, and reproduce them for classroom use. (Domestic) #3 1 30 $467 (Outside U.S.) #3 1 30 $467 Institutional Membership (Print Only) Institutional Memberships receive print copies of The UMAP Journal quarterly, our annual CD collection UMAP Modules, Tools for Teaching , and our organizational newsletter Consortium . (Domestic) #3 1 40 $312 (Outside U.S.) #3 1 41 $351 Institutional Plus Membership (Print Plus Web) Institutional Plus Memberships receive print copies of the quarterly issues of The UMAP Journal , our annual CD collection UMAP Modules, Tools for Teaching , our organizationalnewsletter Consortium , and online membership that allows members to search our online catalog, download COMAP print materials, and reproduce them for classroom use. (Domestic) #3 1 70 $615 (Outside U.S.) #3 1 71 $659For individual membership options visitwww.comap.comfor more information.To order, send a check or money order to COMAP, or call toll-free 1-800-77-COMAP (1-800-772-6627). 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 coop-eration 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 Re-search and the Management Sciences (INFORMS). The Journal acquaints readers with awide variety of professional applications of the mathematical sciences and provides a forumfor the discussion of new directions in mathematical education (ISSN 0197-3622). Periodical rate postage paid at B edford , MA and at additional mailing offices. Send address changes to: info@comap.com COMAP, Inc., Suite 3B, 175 Middlesex Tpke., Bedford, MA, 01730 © Copyright 201 1  by COMAP, Inc. All rights reserved. Mathematical Contest in Modeling (MCM) ® , High School Mathematical Contest inModeling (HiMCM) ® , and Interdisciplinary Contest in Modeling(ICM) ® are registered trade marks of COMAP, Inc.  Vol. 32, No. 2 2010Table of ContentsPublisher’s Editorial Good Ideas, Tireless Efforts Solomon A. Garfunkel ...............................................................93 Editor’s Note Errata to Genetic Inversion Module  ...............................................98 MCM Modeling Forum Results of the 2011 Mathematical Contest in Modeling Frank R. Giordano.....................................................................99 A Half-Blood Half-Pipe, A Perfect Performance Enhao Gong, Xiaoyun Wang, and Rongsha Li ........................... 109 Judges’ Commentary: The Outstanding Snowboard CoursePapers Kelly Black.............................................................................. 123 Fewest Repeaters for a Circular Area:Iterative Extremal Optimization Based on Voronoi Diagrams Wenqiang Wang, Yue Cao, and Zimo Yang................................ 131 Judges’ Commentary: The Outstanding Repeater CoordinationPapers Kathleen Shannon ................................................................... 149 Judges’ Commentary: The Fusaro Award for theRepeater Coordination Problem Marie Vanisko ......................................................................... 155 ICM Modeling Forum Results of the 2011 InterdisciplinaryContest in Modeling Chris Arney ............................................................................ 159 Electric Cars as a Widespread Means of Transportation Zachary Stanko, Brenda Howell, and Rick Bailey....................... 165 Author’s Commentary: The Marine Pollution Problem Miriam C. Goldstein ................................................................ 175 Judges’ Commentary: The Outstanding Electric Car Papers  John Kobza and Rodney Sturdivant.......................................... 179  Publisher’s Editorial  93 Publisher’s Editorial Good Ideas, Tireless Efforts Solomon A. Garfunkel Executive DirectorCOMAP, Inc.175 Middlesex Turnpike, Suite 3BBedford , MA 01730–1459 s.garfunkel@mail.comap.com Aftertheconclusionofthisyear’sMathematicalContestinModeling R   ,I and others deeply involved in the Contest received the following fromContest Director Frank Giordano:Dear Friends of the MCM,It has been my pleasure to be the Contest Director of the MCM forthe past 20 contests. At the end of this year’s contest, I am delightedthatthecontestdirectorshipwillbeintheableandenthusiastichandsof Bill Fox.I would like to thank all of you for your continued support of theMCM over the years: beginning with Ben Fusaro, the founder of thecontest, Sol Garfunkel and COMAP for sponsoring the contest, andfounding fathers Marvin Keener and Maynard Thompson who have beenattheFinalJudgingsincethebeginning. Iwouldalsoliketothank Courtney Coleman and Bob Borrelli for hosting the Final Judging atClaremont for many years. We remember fondly Mike Moody for hissupport, friendship, and warm hospitality. And who can forget Bob’swonderfulwinetastings! Morerecently,wethankGordonMcCormick and the Naval PostgraduateSchool(NPS) for hostingand sponsoringus and facilitating our work.Isincerelyappreciatethecounsel,wisdom,andleadershipofMar-vinKeenerandMaynardThompson,whohaveservedasHeadJudgeseach of the last 20 years. They helped make my job both easy and en- joyable. Their leadership during all phases of the contest has beenspectacular.I taught at West Point with Pat Driscoll and Bill Fox. Drawing onthatexperience,theyknewIwouldneedhelp,andtheywillinglygave The UMAP Journal  32 (2) (2011) 93–98. c  Copyright 2011 by COMAP, Inc. All rights reserved.Permission to make digital or hard copies of part or all of this work for personal or classroom useis granted without fee provided that copies are not made or distributed for profit or commercialadvantage and that copies bear this notice. Abstracting with credit is permitted, but copyrightsfor 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.  94  The UMAP Journal 32.2 (2011) it as Associate Directors. Additionally, as the number of contestants began to increase, Pat headed up the Regional Judging at West Pointwhile Bill did the same at NPS with both sites accomplishing hugeamounts of work in a short period of time, always with good cheer.Pat and Bill would often stay late and come early at the Final Judgingas well to solve software problems and anything else that needed to be done. Their professional and dedicated service has allowed thecontest to expand and take on new challenges without degrading thehigh standards of the contest. Thank you!Iwouldespeciallyliketothankourfacultyadvisorsfororganizing,training,andmotivatingtheirteams. Havingbeenafacultyadvisoronthefirstseveralcontests,I knowthatthejobrequires devotionbutis avery rewarding experience for the dedicated educator. Additionally,we entrust the faculty advisor with the enormous responsibility toensure compliance with the contest rules. Thank you for establishingthe spirit of fair competition that has characterized our contest. Overthe years, I have met or spoken with many of you. I appreciate yourcamaraderieandfeedbackthathasallowedustocontinuallyexamineand improve our rules and procedures. Additionally, the feedback Ihavegottenfrompastandpresentcontestantsishightestimonytothedifference that you have made in their lives. A heartfelt thanks to allof you!AmajordecisionbyCOMAPwastoallowunlimitedparticipation by the schools and provide optional feedback to the students and fac-ulty advisors. The number of contestants increased rapidly from acouple hundred to about 3,600 this year. COMAP felt that if studentswould devote 96 hours to solving an interesting problem, we should be able to find folks willing to judge their work and provide usefulfeedback if the teams asked for it. Participation and feedback are cer-tainlynoblegoalsthatwewantedtoattainwithoutanylossinquality.This challenge was met due to the hard work at our triage sites, in-cluding at Appalachian State University under the leadership of BillBauldry, the National Security Agency (NSA) led by Peter Anspach,Carroll College led by Marie Vanisko, West Point led by Pat Driscoll,and NPS led by Bill Fox. I give my heartfelt thanks to each of the judgeswhovolunteeredtheirtimeatthosesites. AlsoatCarroll,SteveHarper deserves special recognition for designing and constantly im-proving the contest software that allows us to enter and process largeamounts of information quickly and assign stratified judging assign-ments based upon the history of each paper. With all the elements inplace, we found that we could converge to the very top papers, theFinalists as we now call them, without loss of quality. Problem C has becometheindependentInterdisciplinaryContestinModelingunderthe wise and able leadership of Chris Arney, who has provided inter-esting problems featuring a variety of associated disciplines. Thanks
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