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Suppose a farmer has 1,000 feet of fence and wishes to build two identical rectangular enclosures. What should be the dimensions of each enclosure if the total area is to be a maximum?

Set problem up and solve using derivatives.

  • appliedcalculus -

    if the sides are x,y

    a = 2xy
    now, 4x+4y=1000, so y=250-x and so
    a = 2x(250-x) = 500x - 2x^2
    da/dx = 500-4x
    da/dx=0 when x=125

    so, the enclosures are both squares, 125x125

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