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Math Help - Find the shortest length of fence....

  1. #1
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    Find the shortest length of fence....

    A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

    I can see that 3x + 2y = The length we want

    and that xy = Area....

    but where do I go from here?
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  2. #2
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    Quote Originally Posted by derekjonathon View Post
    A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

    I can see that 3x + 2y = The length we want

    and that xy = Area....

    but where do I go from here?
    xy = 1500000

    solve for x in terms of y or y in terms of x (your choice), and substitute into your length equation to get L in terms of a single variable. Take the derivative and minimize.


    I recommend you visit this site ...

    http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html

    ... to gain some knowledge of optimization using calculus.
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