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Math Help - Shortest fence distance

  1. #1
    Junior Member mant1s's Avatar
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    Shortest fence distance

    Hi All,

    Could someone please help me with what I am doing wrong with this optimization problem?...

    Code:
    A rancher wants to fence in an area of 2000000 
    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?
    My Work..

    Code:
    2000000 = ab ---> b = 2000000/a
    
    L = 3a + 2b = 3a + 4000000/a
    
    0 = L' = 3 - 4000000 / a^2
    
    a = 3651.48ft
    
    b = 4000000/ 3651.48 = 1095.45ft
    
    Lmin = 3(3651.48) + 2(1095.45) =!?  13145.3ft
    
    Any help is appreciated! I was following along with this example:
    http://www.mathhelpforum.com/math-he...n-problem.html

    -M
    Last edited by mant1s; August 2nd 2009 at 05:45 PM.
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  2. #2
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    you put an extra zero in your calculator when you find out a.

    recalculate a and its good
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  3. #3
    Junior Member mant1s's Avatar
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    Haytham, Thanks for looking..

    I did what you said and got 10392.3 for Lmin. However the program I am using is telling me it's the wrong answer. Could you or someone else confirm this?

    Thank you,

    -M
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  4. #4
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    sorry didnt notice

    b=2000000/a

    you used b=4000000/a
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  5. #5
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    mr fantastic's Avatar
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    Quote Originally Posted by mant1s View Post
    Haytham, Thanks for looking..

    I did what you said and got 10392.3 for Lmin. However the program I am using is telling me it's the wrong answer. Could you or someone else confirm this?

    Thank you,

    -M
    Your answer for Lmin is wrong.

    Do you get a = 1154.7 (correct to 1 decimal place)? If not, then you've made a mistake somwhere in your arithmetic.
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  6. #6
    Junior Member mant1s's Avatar
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    yesss!

    6928.2 = Lmin
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  7. #7
    Junior Member mant1s's Avatar
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    Fantastic,

    Yes I did get that for a (1154.7).

    Thanks for taking a look.
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