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Homework Help: Optimization problem

  1. Nov 7, 2005 #1
    Q: A trough is to be made from three planks, each 12 in. wide. If the cross section has the shape of a trapezoid, how far apart should the tops of the sides be placed to give the trough maximum carrying capacity?

    OK the area of a trapezoid is
    I know that much, but I've been struggling with this one, off and on, for about two days. I just don't know where to start. I'm not looking for an answer, just a starting point please. :confused:
  2. jcsd
  3. Nov 8, 2005 #2


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    Homework Helper

    The area of a trapezoid is,

    A = ½(b1 + b2)*h

    where b1 and b2 are the lengths of the parallel sides and h is the perpindicular distance between them.

    You want to maximise this area, so find a relation between h and (b1 and b2) using the angle the side plank is at.

    Then A is a function of the angle. Maximise A wrt the angle.
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