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Math Help - optimization problem(Find minimum fencing,given total area)

  1. #1
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    optimization problem(Find minimum fencing,given total area)

    a rectangular field is going to be enclosed and divided into two separate rectangular areas.(The areas do not have to be equal.)Find the minimum fencing that is required if the total area of the field is 1200m2.
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  2. #2
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    Quote Originally Posted by dcfi6052 View Post
    a rectangular field is going to be enclosed and divided into two separate rectangular areas.(The areas do not have to be equal.)Find the minimum fencing that is required if the total area of the field is 1200m2.
    Are you giving us all the conditions for this problem?

    RonL
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    Yes, that is all of the information that is given.
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    Hello, dcfi6052!

    A rectangular field is going to be enclosed and divided into two separate rectangular areas.
    Find the minimum fencing that is required if the total area of the field is 1200 mē.

    First, make a sketch . . .
    Code:
          : - - - -  x  - - - - :
          *-------*-------------*
          |       |             |
         y|      y|             |y
          |       |             |
          *-------*-------------*
          : - - - -  x  - - - - :

    The area is 1200 mē: . xy \,=\,1200\quad\Rightarrow\quad y \,= \,\frac{1200}{x} [1]

    The total fencing is: . F \:=\:2x + 3y [2]

    Substitute [1] into [2]: . F \:=\:2x + 3\left(\frac{1200}{x}\right)

    Therefore: . F \;=\;2x + 3600x^{-1} is the function to be minimized.

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    Thx Soroban I appriciate the help.
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