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Optimization

AP Calculus AB· difficulty 3/5

A farmer fences three sides of a rectangular plot (the fourth side is a wall) using 4040 m of fencing. Maximum enclosed area?

  • A

    400 m2400~\text{m}^2

  • B

    300 m2300~\text{m}^2

  • C

    100 m2100~\text{m}^2

  • D

    200 m2200~\text{m}^2

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Explanation

w+2h=40w + 2 h = 40, A=whA = w h. Maximize: A=(40−2h)h=40h−2h2A = (40 - 2h) h = 40h - 2h^2. A′=40−4h=0⇒h=10,w=20A' = 40 - 4h = 0 \Rightarrow h = 10, w = 20. A=200 m2A = 200~\text{m}^2.

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