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!

2. 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:
      *-------*-------*-------*
|       |       |       |
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x|      x|      x|      x|
|       |       |       |
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*-------*-------*-------*
: - - - - - 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 . . .