Metodo Simplex 4

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    Luis Medina Aquino

    METODO SIMPLEXCaso en que las restricciones sondel tipo >

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    PROBLEMA

    FORMA CANONICAMaximizar Z = 2 X1 + 4 X2 + 3 X3 Sujeto a:

      - X! X" ! " X# ≤ $  % X & " X" ! " X# ' %

    " X ! " X" ! X# ≥ (

    X) X") X# ≥ *

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    PROBLEMA

    FORMA CANONICAMaximizar Z = 2 X1 + 4 X2 + 3 X3 Sujeto a:

      - X! X" ! " X# ≤  $ +S,  % X & " X" ! " X# ' % +a,

    " X ! " X" ! X# ≥ ( +-S") a",

    X) X") X# ≥ *

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    PROBLEMAMaximizar Z = 2 X1 + 4 X2 + 3 X3

    Sujeto a:  - X ! X" ! " X# $ +S,

      % X - " X" ! " X# ' % +a,  " X ! " X" ! X# > ( +-S") a",

    X) X") X# ≥ *FORMA ESTANDAR

    Maximizar Z = 2 X1 + 4 X2 + 3 X3 + 0 S1 + 0 S2 M a1 M a2

    Sujeto a:- X ! X" ! " X# ! S ! * S" ! * a ! * a" ' $

    % X - " X" ! " X# ! * S ! * S" ! a ! * a" ' %  " X ! " X" ! X# ! * S & S" ! * a ! a" ' (  X) X") X#) S) S") a) a" ≥ *

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B- " * * * $% -" " * * * %" " * - * (

    0 j  

    Cj - 0jCj-0j

    Maximizar Z = 2 X1 + 4 X2 + 3 X3 + 0 S1 + 0 S2 M a1 M a2Sujeto a:

    - X ! X" ! " X# ! S ! * S" ! * a ! * a" ' $% X - " X" ! " X# ! * S ! * S" ! a ! * a" ' % " X ! " X" ! X# ! * S & S" ! * a ! a" ' (

    X) X") X#) S) S") a) a" ≥ *

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j  

    Cj - 0jCj-0j

    .*

    .*"

    .*#

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j -1M * -#M * M -M -M -*M

    Cj - 0jCj-0j

    .*

    .*"

    .*#

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * *Cj-0j

    .*

    .*"

    .*#

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * *Cj-0j

    Colu2napi3ote

    .*

    .*"

    .*#

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * *Cj-0j

    Colu2napi3ote

    .*

    .*"

    .*#

    /o

    %4% '

    (4" ' "

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * *Cj-0j

    Colu2napi3ote

    .*

    .*"

    .*#

    /o

    %4% ' #

    (4" ' "

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * *Cj-0j

    Colu2napi3ote

    .*

    .*"

    .*#

    5ilapi3ote

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    ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1   X2   X3   "1   "2   a1   a2   B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0 j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * *Cj-0j

    .*

    .*"

    .*#

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    -M a" * * 0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    -M a" * * 0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    ." ' .*"4%

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *" X -4# 4# * * 4% *

    -M a" * * 0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    ." ' .*"4%

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *" X -4# 4# * * 4% *

    -M a" * * 0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .' .* ! .".* - " * * * $

    ! ."

    .

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *" X -4# 4# * * 4% *

    -M a" * * 0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .' .* ! .".* - " * * * $

    ! ." -4# 4# * * 4% *

    .

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *" X -4# 4# * * 4% *

    -M a" * * 0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .' .* ! .".* - " * * * $

    ! ." -4# 4# * * 4% *

    . * "4# 64# * 4% * *

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .' .* ! .".* - " * * * $

    ! ." -4# 4# * * 4% *

    . * "4# 64# * 4% * *

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .#' .*# - " .".*# " " * - * (

    -" ."

    .#

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .#' .*# - " .".*# " " * - * (

    -" ." -" "4# -"4# * * -4# * -"

    .#

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .#' .*# - " .".*# " " * - * (

    -" ." -" "4# -"4# * * -4# * -"

    .# * 14# 4# * - -4# "

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    .#' .*# - " .".*# " " * - * (

    -" ." -" "4# -"4# * * -4# * -"

    .# * 14# 4# * - -4# "

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"MCj - 0j Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (

    0j -1M * -#M * M -M -M -*MCj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"MCj - 0j *

    +(!1M,# 64#!M4# * -M -4#-(M4# * Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (0j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"MCj - 0j *

    +(!1M,# 64#!M4# * -M -4#-(M4# * Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    Colu2napi3ote

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (0j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"MCj - 0j *

    +(!1M,# 64#!M4# * -M -4#-(M4# * Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    Colu2napi3ote

    *4+"4#,'7/o"4+14#, ' #4(

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (0j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"MCj - 0j *

    +(!1M,# 64#!M4# * -M -4#-(M4# * Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    Colu2napi3ote

    *4+"4#,'7/o"4+14#, ' 8 # 

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      ITE.ACIO/ *  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s - " * * * $

    -M a % -" " * * * %-M a" " " * - * (0j -1M * -#M * M -M -M -*M

    Cj - 0j "!1M ( #!#M * -M * * Cj-0j *

    .*

    .*"

    .*#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"MCj - 0j *

    +(!1M,# 64#!M4# * -M -4#-(M4# * Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    Colu2napi3ote

    5ila

    pi3ote

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      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *" X -4# 4# * * 4% *

    -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"MCj - 0j *

    +(!1M,# 64#!M4# * -M -4#-(M4# * Cj-0j *

    ITE.ACIO/

    .

    ."

    .#

    Colu2napi3ote

    5ila

    pi3ote

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      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "

    0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    ( X" * *0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

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      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    ( X" * *0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ."#' .# 9 #41

  • 8/18/2019 Metodo Simplex 4

    34/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    ( X" * 41 * -#41 -41 #41 #4(0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ."#' .# 9 #41

  • 8/18/2019 Metodo Simplex 4

    35/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    ( X" * 41 * -#41 -41 #41 #4(0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ."' . -"4# ."#. * "4# 64# * 4% * *

    -"4# ."#

    ."

  • 8/18/2019 Metodo Simplex 4

    36/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    ( X" * 41 * -#41 -41 #41 #4(0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ."' . -"4# ."#. * "4# 64# * 4% * *

    -"4# ."# * -"4# -4" * 4( 4" -4( -4"

    ."

  • 8/18/2019 Metodo Simplex 4

    37/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s * *

    " X * *

    ( X" * 41 * -#41 -41 #41 #4(0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ."' . -"4# ."#. * "4# 64# * 4% * *

    -"4# ."# * -"4# -4" * 4( 4" -4( -4"

    ." * * $4( 4( 4( -4( $4"

  • 8/18/2019 Metodo Simplex 4

    38/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * *( X" * 41 * -#41 -41 #41 #4(

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ."' . -"4# ."#. * "4# 64# * 4% * *

    -"4# ."# * -"4# -4" * 4( 4" -4( -4"

    ." * * $4( 4( 4( -4( $4"

  • 8/18/2019 Metodo Simplex 4

    39/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * *( X" * 41 * -#41 -41 #41 #4(

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    .""' ." !4# ."#." -4# 4# * * 4% *

    !4# ."#

    .""

  • 8/18/2019 Metodo Simplex 4

    40/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * *( X" * 41 * -#41 -41 #41 #4(

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    .""' ." !4# ."#." -4# 4# * * 4% *

    !4# ."# * 4# 4"( * -41 -4"( 41 4(

    .""

  • 8/18/2019 Metodo Simplex 4

    41/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * *( X" * 41 * -#41 -41 #41 #4(

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    .""' ." !4# ."#." -4# 4# * * 4% *

    !4# ."# * 4# 4"( * -41 -4"( 41 4(

    ."" * #41 * -41 41 41 74(

  • 8/18/2019 Metodo Simplex 4

    42/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    ."

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0jCj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    .""' ." !4# ."#." -4# 4# * * 4% *

    !4# ."# * 4# 4"( * -41 -4"( 41 4(

    ."" * #41 * -41 41 41 74(

    ITE.ACIO/

  • 8/18/2019 Metodo Simplex 4

    43/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    .

    "

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0j " ( 74( * -64( -4( 64( 4"Cj - 0j Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ITE.ACIO/

  • 8/18/2019 Metodo Simplex 4

    44/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    .

    "

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0j " ( 74( * -64( -4( 64( 4"Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    ITE.ACIO/

  • 8/18/2019 Metodo Simplex 4

    45/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    .

    "

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0j " ( 74( * -64( -4( 64( 4"Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    Colu2napi3ote

    ITE.ACIO/

  • 8/18/2019 Metodo Simplex 4

    46/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    .

    "

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0j " ( 74( * -64( -4( 64( 4"Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    Colu2napi3ote

    +$4",4+4(,/o/o

    ITE.ACIO/

  • 8/18/2019 Metodo Simplex 4

    47/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    .

    "

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0j " ( 74( * -64( -4( 64( 4"Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    Colu2napi3ote

    #1  /o/o

    ITE.ACIO/

  • 8/18/2019 Metodo Simplex 4

    48/63

      ITE.ACIO/   Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * "4# 64# * 4% * *

    " X -4# 4# * * 4% * -M a" * 14# 4# * - -4# "0j " -"4#-1M4# "4#-M4# * M 4#!M4# -M "-"M

    Cj - 0j *+(!1M,

    # 64#!M4# * -M -4#-(M4# * Cj-0j *

    .

    .

    "

    .#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0j " ( 74( * -64( -4( 64( 4"Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    Colu2napi3ote

    5ilapi3ote

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    49/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "

    ."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"" X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(

    0j " ( 74( * -64( -4( 64( 4"Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ITE.ACIO/ "

    ."

    .""

    ."#

    Colu2napi3ote

    5ilapi3ote

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    50/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s" * *

    " X * *

    ( X" * *0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    51/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B

    * s" * *

    " X * *

    ( X" * *0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .# ' ." 9 (

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    52/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1

    " X * *

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .# ' ." 9 (

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    53/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1

    " X * *

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .#"' ."" !41 .#."" * #41 * -41 41 41 74(

    !41 .#

    .#

    "

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    54/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1

    " X * *

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .#"' ."" !41 .#."" * #41 * -41 41 41 74(

    !41 .# * * $41 4" 41 41 -41 $4(

    .#"

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    55/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1

    " X * *

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .#"' ."" !41 .#."" * #41 * -41 41 41 74(

    !41 .# * * $41 4" 41 41 -41 $4(

    .#" * #4" 4" * 4( * %

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    56/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1" X * #4" 4" * 4( * %

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .#"' ."" !41 .#."" * #41 * -41 41 41 74(

    !41 .# * * $41 4" 41 41 -41 $4(

    .#" * #4" 4" * 4( * %

    ITE.ACIO/ "

  • 8/18/2019 Metodo Simplex 4

    57/63

      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1" X * #4" 4" * 4( * %

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .##' ."# !#41 .#."# * 41 * -#41 -41 #41 #4(

    !#41 .#

    .#

    #

    ITE.ACIO/ "

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      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1" X * #4" 4" * 4( * %

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .##' ."# !#41 .#."# * 41 * -#41 -41 #41 #4(

    !#41 .# * * "641 #4" #41 #41 -#41 764(

    .##

    ITE.ACIO/ "

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      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1" X * #4" 4" * 4( * %

    ( X" * *

    0j

    Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .##' ."# !#41 .#."# * 41 * -#41 -41 #41 #4(

    !#41 .# * * "641 #4" #41 #41 -#41 764(

    .## * 64" #4" * 4( * 7

    ITE.ACIO/ "

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      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1" X * #4" 4" * 4( * %( X" * 64" #4" * 4( * 7

    0jCj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    .##' ."# !#41 .#."# * 41 * -#41 -41 #41 #4(

    !#41 .# * * "641 #4" #41 #41 -#41 764(

    .## * 64" #4" * 4( * 7

    ITE.ACIO/ "

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      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1" X * #4" 4" * 4( * %( X" * 64" #4" * 4( * 7

    0j " ( 6 6 * #4" * 6"Cj - 0j Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    ITE.ACIO/ "

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      ITE.ACIO/ "  Cj " ( # * * -M -M

    CB !B X1 X2 X3 "1 "2 a1 a2 B* s * * $4( 4( 4( -4( $4"

    " X * #41 * -41 41 41 74(( X" * 41 * -#41 -41 #41 #4(0j " ( 74( * -64( -4( 64( 4"

    Cj - 0j * * 64( * 64( -M!4( -M-64( Cj-0j *

    ."

    ."

    "."#

      Cj " ( # * * -M -MCB !B X1 X2 X3 "1 "2 a1 a2 B* s" * * $ ( - #1" X * #4" 4" * 4( * %( X" * 64" #4" * 4( * 7

    0j " ( 6 6 * #4" * 6"Cj - 0j * * -( -6 * -#4"-M -M Cj-0j *

    ITE.ACIO/ #

    .#

    .#"

    .##

    ;a que todos los Cj & 0j * entonces la ta

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    @.ACIAS

    Ing.Luis

    Medina