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Optimization Problem (Calc I)

  1. Oct 16, 2005 #1
    I am having trouble setting up the primary equation to this optimization problem.

    Here is a link to the problem
    http://img293.imageshack.us/img293/806/appliedminmaxprob5vo.jpg" [Broken]

    Here is the best equation I can come up with but this leads me nowhere...

    The hypotenuse of the each triangle: sqrt(x^2+y^2)
    The length of the line from (0,h) to (0,y): h-y

    let L be the length of the wire needed then

    L = 2sqrt(x^2+y^2)+h-y

    2sqrt(x^2+y^2) for the two hypotenuses of the triangles
    h-y for the small line segment from point (0,h) to (0,y)

    Where can I go from here? I'm only looking for a small hint to get me going in the right direction... Thanks
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 16, 2005 #2


    User Avatar
    Homework Helper

    Looks good so far. The clue for the next step is in the question, which is to find y such that the length of power line is minimized. Hint: a derivative is involved.
  4. Oct 17, 2005 #3


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    Staff Emeritus
    Science Advisor

    Remember that x and h are given constants. It is only y that is a variable. Your answer will depend on x and h.
  5. Oct 17, 2005 #4
    Here is my final solution so far...
    It's 5 pages but I tried to explain what I was doing in detail :)
    Please comment on my mathematical writing as well as my solution.
    I really want to improve my mathematical writing.

    http://img434.imageshack.us/img434/6807/solutionpart16fp.jpg" [Broken]

    http://img434.imageshack.us/img434/9853/solutionpart26xc.jpg" [Broken]

    http://img434.imageshack.us/img434/4665/solutionpart39cr.jpg" [Broken]

    http://img434.imageshack.us/img434/2691/solutionpart41om.jpg" [Broken]

    http://img434.imageshack.us/img434/1182/solutionpart56qq.jpg" [Broken]

    /math rocks
    //off to watch The Daily Show
    ////why am i doing this
    /////I read to much fark.com
    Last edited by a moderator: May 2, 2017
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