1. ## Maximum

A farmer has 100 yards of fencing to form 2 identical rectangular pens and a third pen that is twice as long as the other 2 pens. All three pens have the same width, x. Which value of y produces the maximum total fenced area?

2. Originally Posted by CalculusKing
A farmer has 100 yards of fencing to form 2 identical rectangular pens and a third pen that is twice as long as the other 2 pens. All three pens have the same width, x. Which value of y produces the maximum total fenced area?
all separate pens, I assume?

1st pen ... $P_1 = 2(x+y)$

2nd pen ... $P_2 = 2(x+y)$

3rd pen ... $P_3 = 2(x + 2y)$

$P_1 + P_2 + P_3 = 100$

$A = xy + xy + x \cdot 2y = 4xy$

use the perimeter equation to solve for x in terms of y, then sub into the area equation ... then maximize.