Optimization problem

  • Thread starter griffon
  • Start date
  • #1
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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
A=2bh
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:
 

Answers and Replies

  • #2
Fermat
Homework Helper
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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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