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Math Help - another LP question

  1. #1
    Junior Member
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    another LP question

    there are 3 electorates, A B C. Gov wants to distribute funds according to.

    let x,y,x=number in millions that electorate A,B,C receive.

    cost=x+y+z,

    total should not exceed 48 million, A should receive no less then 10 million, B should receive at least 5million more then C, and C should receive at least the average received by A and B. Then minimize the cost of the gov payouts.

    Minimize: c=x+y+z
    subject to: x>=10
    x+y+z<=48
    y-5x>=0
    z-x/2-y/2>=0
    x,y,z>=0
    I dont think this is right, and there is a mistake somewhere but cant find it.
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  2. #2
    Super Member Aryth's Avatar
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    First, state the problem:

    We are going to minimize c = x + y + z under the constraint that x \geq 10. So we get a system of equations:

    x + y + z \leq 48 (Total Should Not Exceed 48 Million.)

     x - z \geq 5 (B should receive at least 5 Million more than C, which means that their difference must be greater than or equal to 5 Million.)

    z \geq \frac{x + y}{2}

    2z - x - y \geq 0 (C should receive at least the average received by A and B. This means that x and y taken from 2 times z should be greater than or equal to 0.)

    Try solving the problem with this set up. If you have anymore questions feel free to ask.
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