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2000年美国中学生数学建模试题及特等奖论文下载 HiMCM Outstanding Papers

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    2000 HiMCM Problem A
    Bank Robbers


    Problem:

    The First National Bank has just been robbed (the position of the bank on the map is marked).  The clerk pressed the silent alarm to the police station.  The police immediately sent out police cars to establish road blocks at the major street junctions leading out of town.  Additionally, 2 police cars were dispatched to the bank.> >>>

    Map information:  (see the series of two maps below)> >>>

    The Bank is located at the corner of 8th Ave. and Colorado Blvd. and is marked with the letter B.  The main exits where the two road blocks are set up are at the intersection of Interstate 70 and Colorado Blvd, and Interstate 70 (past Riverside Drive).  These are marked with a RB1 and RB2 symbol.> >>>

    • Assume the robbers left the bank just before the police cars arrived.  Develop an efficient algorithm for the police cars to sweep the area in order to force the bank robbers (who were fleeing by car) into one of the established road blocks. > >

    • Assume that no cars break down during the chase or run out of gas.> >>>

    • Further assume that the robbers do not decide to flee via other transportation means.  

    11.jpg


    2000 HiMCM Problem B
    Elections

     

    Problem:

    It is almost election time and it is time to revisit the electoral vote process. The constitution and its amendments have provided a subjective method for awarding electoral votes to states. Additionally, a state popular vote, no matter how close, awards all electoral votes to the winner of that plurality. Create a mathematical model that is different than the current electoral system. Your model might award fractional amounts of electoral votes or change the methods by which the number of electoral votes are awarded to the states. Carefully describe your model and test its application with the data from the 1992 election. Justify why your model is better than the current model?

    1992 Election Summary> >>>

    State                         Electoral Vote                                Popular Vote> >

    State> >

    Clinton> >

    Bush> >

    Perot

    Clinton

    Bush

    Perot

    AL

    0

    9

    0

    668146

    797477

    180209

    AK

    0

    3

    0

    57264

    73683

    50034

    AZ

    0

    8

    0

    521736

    543876

    339307

    AR

    6

    0

    0

    495150

    331867

    97549

    CA

    54

    0

    0

    4812317

    3338942

    2144856

    CO

    8

    0

    0

    625402

    557408

    362506

    CT

    8

    0

    0

    681081

    574738

    348028

    DE

    3

    0

    0

    125997

    102436

    59061

    DC

    3

    0

    0

    186301

    19813

    9284

    FL

    0

    25

    0

    2051205

    2131263

    1040953

    GA

    13

    0

    0

    1002433

    985682

    306489

    HI

    4

    0

    0

    178893

    136430

    52863

    ID

    0

    4

    0

    136249

    201787

    129897

    IL

    22

    0

    0

    2378873

    1717736

    832307

    IN

    0

    12

    0

    839227

    978627

    451858

    IA

    7

    0

    0

    583937

    503338

    251040

    KS

    0

    6

    0

    386168

    443314

    312670

    KY

    8

    0

    0

    661059

    617419

    203587

    LA

    9

    0

    0

    815305

    729880

    210604

    ME

    4

    0

    0

    261859

    207122

    205076

    MD

    10

    0

    0

    941979

    671609

    271198

    MA

    12

    0

    0

    1315016

    803974

    630440

    MI

    18

    0

    0

    1854603

    1585251

    819931

    MN

    10

    0

    0

    994843

    734845

    549517

    MS

    0

    7

    0

    391911

    478878

    83950

    MO

    11

    0

    0

    1051328

    810058

    517918

    MT

    3

    0

    0

    153899

    143702

    106735

    NE

    0

    5

    0

    214106

    338646

    171938

    NV

    4

    0

    0

    185401

    171378

    129532

    NH

    4

    0

    0

    207264

    199623

    120029

    NJ

    15

    0

    0

    1361088

    1303686

    504152

    NM

    5

    0

    0

    255558

    209467

    90653

    NY

    33

    0

    0

    3244562

    2240050

    1028607

    NC

    0

    14

    0

    1103716

    1122608

    353845

    ND

    0

    3

    0

    97546

    133911

    69805

    OH

    21

    0

    0

    1964842

    1876445

    1024319

    OK

    0

    8

    0

    473066

    592929

    319978

    OR

    7

    0

    0

    524161

    393273

    307244

    PA

    23

    0

    0

    2233810

    1777372

    895563

    RI

    4

    0

    0

    198877

    121864

    94717

    SC

    0

    8

    0

    475313

    572031

    137598

    SD

    0

    3

    0

    124861

    136671

    73297

    TN

    11

    0

    0

    933618

    840897

    199787

    TX

    0

    32

    0

    2278912

    2460201

    1349644

    UT

    0

    5

    0

    182590

    320462

    202578

    VT

    3

    0

    0

    125803

    85512

    61510

    VA

    0

    13

    0

    1033825

    1146909

    344840

    WA

    11

    0

    0

    855710

    609912

    470239

    WV

    5

    0

    0

    324009

    236526

    105652

    WI

    11

    0

    0

    1035942

    926245

    542610

    WY

    0

    3

    0

    67863

    79558

    51209

    TOTALS

    370

    168

    0

    43682624

    38117331

    19217213

    2000 HiMCM Outstanding Papers.pdf

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