Posted by **Grant** on Friday, February 24, 2012 at 12:08am.

A farmer with 700 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

- Calc 1 -
**Grant**, Friday, February 24, 2012 at 12:55am
Answer is 12250

- Calc 1 -
**Steve**, Friday, February 24, 2012 at 10:49am
so, is there a question somewhere in there?

- Calc 1 -
**MathMate**, Friday, February 24, 2012 at 1:43pm
What is the largest possible total area of the four pens?

Let x=shorter side of the big rectangle.

and y=long side of the big rectangle

Fence required = 5x+2y=700 => y=350-5x/2

Total area of pens

A=xy

=x(350-5x/2)

To get the maximum area, we equate dA/dx=0

dA/dx = 350-5x = 0, or

x=70

y=350-5x/2 = 175

Maximum total area=xy=70*175=12250'

- Calc 1 -
**Tina**, Wednesday, April 17, 2013 at 1:06pm
Can someone draw the picture?

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