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Math Help - Please Help maximize!!

  1. #1
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    Please Help maximize!!

    A farmer has 3,000 feet of fence to enclose a rectangular field and subdivide it into 3 rectangular plots. If x denotes the width of the field and y the length, find the value of x so that the total area of the field is maximized!
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  2. #2
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    Hello, 0017024651!

    A farmer has 3,000 feet of fence to enclose a rectangular field
    and subdivide it into 3 rectangular plots.
    If x denotes the width of the field and y the length,
    find the value of x so that the total area of the field is maximized.
    Code:
          *-------*-------*-------*
          |       |       |       |
          |       |       |       |
         x|      x|      x|      x|
          |       |       |       |
          |       |       |       |
          *-------*-------*-------*
          : - - - - - y - - - - - :

    He has four fences which are x feet long
    . . and two fences which are y feet long.
    So total fencing is: . 4x + 2y \:=\:3000\quad\Rightarrow\quad y \:=\:1500-2x .[1]

    The area of the field is: . A \:=\:xy .[2]

    Substitute [1] into [2]: . A \;=\;x(1500-2x) \quad\Rightarrow\quad A \;=\;1500x-2x^2

    And that is the function we must maximize . . .

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