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Another cool optimization problem

  1. Apr 21, 2008 #1
    1. The problem statement, all variables and given/known data

    find the dimensions of a rectangle with perimeter 100m whose area is as large as possible


    2. Relevant equations

    area = XY

    100 = 2x + 2y

    y= 100/4x

    x(100/4x)

    (400x - 400x)/16x^2

    1/16x^2 = 0
    3. The attempt at a solution

    well........
    am lost
     
  2. jcsd
  3. Apr 21, 2008 #2

    exk

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    y=100/4x, reconsider that step. You are having the same trouble as in your other question. You need to be more careful in your algebra/arithmetic.
     
  4. Apr 21, 2008 #3
    2y = 100/2x

    y = (100/2x) * .5
     
  5. Apr 21, 2008 #4

    exk

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    How are you getting from 100=2x+2y to 2y=100/2x?
     
  6. Apr 21, 2008 #5
    am trying to solve for y
     
  7. Apr 21, 2008 #6
    y = (100/2)-x
     
  8. Apr 21, 2008 #7

    exk

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    Ok that's better (100/2=50).

    So what's the next step.
     
  9. Apr 21, 2008 #8
    find the derivates of 50x-x^2
    50-2x=0
    x=25
    100=2(25)+2y
     
  10. Apr 21, 2008 #9
  11. Apr 21, 2008 #10

    exk

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    Yep, that's it.
     
  12. Apr 21, 2008 #11
    thanks alot. care for one more problem?
     
  13. Apr 21, 2008 #12

    Dick

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    Science Advisor
    Homework Helper

    Suggest you start a new thread. Some people don't pay much attention to threads with large numbers of posts. Including me, usually. This is an exception.
     
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