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A rancher wants to make a rectangular pen to house her animals. She will divide it up with 3 fences down the middle parallel to one side. If she has 14000 ft of fencing to work with, what are the dimensions of the pen of greatest area?
Width =
Length =

What is the greatest area pen that the rancher can make?
Area =

  • Calculus -

    a = xy = x(14000-2x)/5
    da/dx = 2800 - 4x/5
    da/dx=0 when x = 3500

    so, the pen is 3500x1400

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