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Math Help - Linear problem, need a little help. :)

  1. #1
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    Linear problem, need a little help. :)

    Ok i have this homework set for my A level H.W and i need a little help on finding the objctive function.

    question =

    100x + 150y

    4x + 4y </= 600
    x + 6y </= 480
    x,y >/= 0

    Note: </= is less than or equal to for this example

    I'm stuck on finding this part of the question

    100x + 150y

    i've put in a number which both goes into

    100x + 150y = 300
    which leaves me with x=3, y=2

    and when i plot that onto a graph it doesn't fit well because all the other answers are much larger.

    Any help would be great!

    thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by entrepreneurforum.co.uk View Post
    Ok i have this homework set for my A level H.W and i need a little help on finding the objctive function.

    question =

    100x + 150y

    4x + 4y </= 600
    x + 6y </= 480
    x,y >/= 0

    Note: </= is less than or equal to for this example

    I'm stuck on finding this part of the question

    100x + 150y

    i've put in a number which both goes into

    100x + 150y = 300
    which leaves me with x=3, y=2

    and when i plot that onto a graph it doesn't fit well because all the other answers are much larger.

    Any help would be great!

    thanks
    This is a linear program the constraints:

    4x + 4y </= 600
    x + 6y </= 480
    x,y >/= 0

    define a feasible region, and the objective to be maximised is

    O(x,y)=100x + 150y

    Now the for a linear program the objective achives its maximum at a vertex of the feasible region unless it is parallel to an edge when it achives its maximum all along the edge.

    So here we find all the vertices of the feasible region and evaluate the objevtive at them and the one where the objective is largest is the optimal point (if two of them both give the maximum of the objective then all the points along the edge of the feasible region conecting those vertices are optima).

    CB
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