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Math Help - optimization

  1. #1
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    optimization

    A farmer wants to fence an area of 1,000,000 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What is the length, in feet, of the shortest side of the rectangle?
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  2. #2
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    Nov 2007
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    Let the length be 'l', width be 'w', and perimeter be 'p'.

    We have:

    lw = 1,000,000.

    And p = 2l + 2w.

    We can re-arrange the first:

    w = 1,000,000/l.

    And substitute in the second:

    p = 2l + 2,000,000/l.

    Finding dp/dl and letting it equal 0 will give you a minimum length. Can you continue?
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