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Math Help - function min/max value (using geometric interpretation)

  1. #1
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    function min/max value (using geometric interpretation)

    a) Find function  f=(x_1-4)^2+(x_2-3)^2 ,where  x_1, x_2\ge 0 and restrictions are: \begin{cases}<br />
    2x_1+3x_2\ge 6 \\<br />
    3x_1-2x_2\le 18\\<br />
    -x_1+2x_2\le8<br />
\end{cases}
    min and max value using task geometric interpretation.


    b) Find:  max f=3x_1+4x_2 ,where  x_1, x_2\ge 0 and restrictions are:
    \begin{cases}<br />
   x_1^2+x_2^2\le 25 \\<br />
   x_1 * x_2\ge 4<br />
\end{cases}
    using geometric interpretation.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Bernice View Post
    a) Find function  f=(x_1-4)^2+(x_2-3)^2 ,where  x_1, x_2\ge 0 and restrictions are: \begin{cases}<br />
2x_1+3x_2\ge 6 \\<br />
3x_1-2x_2\le 18\\<br />
-x_1+2x_2\le8<br />
\end{cases}
    min and max value using task geometric interpretation.
    Your objective is:

    r^2= f=(x_1-4)^2+(x_2-3)^2

    So your question is asking you to find the point in the feasible region furtherest from (4,3) and evaluate the objective there.

    CB
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