Calc 1

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A farmer with 700 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

  • Calc 1 -

    Answer is 12250

  • Calc 1 -

    so, is there a question somewhere in there?

  • Calc 1 -

    What is the largest possible total area of the four pens?

    Let x=shorter side of the big rectangle.
    and y=long side of the big rectangle

    Fence required = 5x+2y=700 => y=350-5x/2

    Total area of pens
    A=xy
    =x(350-5x/2)

    To get the maximum area, we equate dA/dx=0

    dA/dx = 350-5x = 0, or

    x=70
    y=350-5x/2 = 175

    Maximum total area=xy=70*175=12250'

  • Calc 1 -

    Can someone draw the picture?

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