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Math Help - Maximum

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    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?
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    Quote Originally Posted by CalculusKing View Post
    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.
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