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Optimization Question

  1. Mar 28, 2010 #1
    Hi, I am having a hard time with this Optimization question as i do not know where to begin, I drew a diagram but what formulas, function etc do I use to start the question? And How do i do it?

    Two towns A and B are 7km and 5km, respectively, from a railroad line. The points C and D nearest to A and B on the line are 8 km apart. Where should the station be located to minimize the length of a new road from A to S to B?

    Here is the Diagram i drew:

    http://img109.imageshack.us/img109/7071/diagramv.png [Broken]

    How would I start going about doing this problem?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 28, 2010 #2

    Office_Shredder

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    Can you write the length of the road as a function of where S is? (in particular, think of S as being the distance from point C)
     
  4. Mar 28, 2010 #3
    See I cant tell if Point CS = 4km and point SD = 4km
    I am not sure if they are both equivalent or not?
    Im confused at this point.

    I know the diagram is right because my teacher was helping me on that part.
     
  5. Mar 28, 2010 #4

    hotvette

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    I think you are trying to jump ahead. S (i.e. distance from C to the station as Office Shredder suggested) is the unknown. By the diagram you drew, the optimal value of S is somewhere between 0 and 8km. If you write an equation L = f(S) where L is the length of the road you are trying to minimize, then it's a matter of setting the derivative of L with repect to S equal to zero and solving for S.
     
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