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Math Help - Matrices

  1. #1
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    Matrices

    I have a worksheet of these problems, if someone could walk me through this one, I can figure out the rest.

    Find the maximum value of C=x+3y on the region determined by the constraints {3x+2y<16
    {0<x<4
    {0<y<5.

    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by gretchen View Post
    I have a worksheet of these problems, if someone could walk me through this one, I can figure out the rest.

    Find the maximum value of C=x+3y on the region determined by the constraints {3x+2y<16
    {0<x<4
    {0<y<5.

    Thanks.
    Because x+3y is linear in x and y the maximum value for C occurs at a vertex
    of the feasible region defined by the constraints.

    The attachment shows the feasible region defined by the constraints and the
    coordinates of the vertices.

    For each vertex evaluate x+3y, and the one that gives the largest of these
    values is the maximum value that C can take in the feasible region.

    RonL
    Attached Thumbnails Attached Thumbnails Matrices-gash.jpg  
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  3. #3
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    So, the maximum value would be:

    C=x+3y
    C=2+3(5)
    C=2+15
    C=17

    Right?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by gretchen View Post
    So, the maximum value would be:

    C=x+3y
    C=2+3(5)
    C=2+15
    C=17

    Right?
    Yes.

    The values at the vertices are:

    (0,0): C=0
    (0,5): C=15
    (2,5): C=17
    (4,2): C=10
    (4,0): C=4

    RonL
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