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Math Help - Linear programming (maximizing)

  1. #1
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    Linear programming (maximizing)

    I am not sure whether I have done this right or that my answer is correct. I have a strong feeling that tells me it is not right. Could you please check it for me?

    Minimize
    C = x + y
    subject to the constraints
    1x +7y ≥ 1
    11x + 2y ≥ 1
    x, y ≥ 0

    The answers I got through solving the system geometrically/graphically is that the minimum of C is 0.244360901 and occurs when x = 0.11842105 and y = 0.125939849.
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  2. #2
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    Re: Linear programming (maximizing)

    Hello, Yoodle15!

    I have no idea how you got those ugly decimals . . .


    \text{Minimize: }\:C \:=\: x + y

    \text{Subject to the constraints: }\:\begin{Bmatrix}x +7y \:\ge\:1 \\ 11x + 2y \:\ge\:1 \\ x, y\:\ge\: 0\end{Bmatrix}

    \text{The graph looks like this:}

    Code:
          |::::::
          |::::::::
         Ro:::::::::
          |*:::::::::
          | *:::::::::
          |  *:::::::::
          *   *:::::::::
          |  * *:::::::::
          |     o::::::::::
          |    Q * *::::::::
          |       *   *:::::::
          |        *     *:::::::
        - + - - - - * - - - o - - - -
          |                 P
    \text{The vertices are: }\:\begin{Bmatrix}P: &(1,0) \\ \\[-4mm]  Q: & (\frac{2}{15},\frac{1}{15}) \\ \\[-4mm] R: & (0,\frac{1}{2}) \end{Bmatrix}

    \text{Test them in the }C\text{-function.}
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