Thread: 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!

Hello, 0017024651!

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

Code:

      *-------*-------*-------*
      |       |       |       |
      |       |       |       |
     x|      x|      x|      x|
      |       |       |       |
      |       |       |       |
      *-------*-------*-------*
      : - - - - - y - - - - - :

He has four fences which are feet long
. . and two fences which are feet long.
So total fencing is: . .[1]

The area of the field is: . .[2]

Substitute [1] into [2]: .

And that is the function we must maximize . . .