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Math Help - Eliminating a variable in an LP problem

  1. #1
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    Eliminating a variable in an LP problem

    Hi, I have the following problem that is solved, but I don't know how it gets to it. I'd really appreciate it if someone could show me.

    Well, the LP problem says:

    minimize f = 8x+10y+18z
    subject to
    2/3x+y+2z=20
    0<=x<=9, 0<=y<=15, 0<=z<=3.

    And then my teacher eliminates z, and he gets:

    minimize f=180+2x+y
    subject to
    42<=2x+3y<=60
    0<=x<=9, 0<=y<=15.

    Well, I know how my teacher got to f=180+2x+y, but how did he get 42<=2x+3y<=60? I know 60 comes from 20*3 (to make 2/3 an integer), but I don't know where 42 comes from.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by juanma101285 View Post
    Hi, I have the following problem that is solved, but I don't know how it gets to it. I'd really appreciate it if someone could show me.

    Well, the LP problem says:

    minimize f = 8x+10y+18z
    subject to
    2/3x+y+2z=20
    0<=x<=9, 0<=y<=15, 0<=z<=3.

    And then my teacher eliminates z, and he gets:

    minimize f=180+2x+y
    subject to
    42<=2x+3y<=60
    0<=x<=9, 0<=y<=15.

    Well, I know how my teacher got to f=180+2x+y, but how did he get 42<=2x+3y<=60? I know 60 comes from 20*3 (to make 2/3 an integer), but I don't know where 42 comes from.
    2x+3y+6z=60
    2x+3y=60-6z

    0<=z<=3

    So, 60-18<=2x+3y<=60-0
    42<=2x+3y<=60
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