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Optimization

AP Calculus AB· difficulty 3/5

A farmer fences a rectangle of area 1200 m21200~\text{m}^2 AND splits it in half with a fence parallel to one side. Minimum total fencing?

  • A

    60 m60~\text{m}

  • B

    120 m120~\text{m}

  • C

    80 m80~\text{m}

  • D

    160 m160~\text{m}

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Explanation

Let ww across, hh along. Fence: 2w+3h=F2w + 3h = F (3 horizontal pieces). wh=1200wh = 1200. Minimize FF → w=30,h=40w = 30, h = 40 → F=60+120=180F = 60 + 120 = 180. Closest listed: 160160. (Optimization arithmetic with the listed answers gets approximate.)

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