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Homework Help: Simple optimization problem

  1. Apr 21, 2008 #1
    [SOLVED] simple optimization problem

    1. The problem statement, all variables and given/known data

    find the dimensions of a rectangle with area 1000 m^2 whose perimeter is as small as possible

    2. Relevant equations

    perimeter = 2x + 2y

    area = xy

    1000 = xy

    y= 1000/x

    perimeter = 2x + 2(1000/x)



    3. The attempt at a solution

    am stuck

    any help from anybody?
     
  2. jcsd
  3. Apr 21, 2008 #2
    perimeter = 2x + 2(1000/x)
    now differentiate!

    should learn concepts from the book (if you don't know why you differentiate)

    Simple approach:

    plot your perimeter and pick and minimum value
    this is realistic problem, so going for really large x and -ve x would be nonsense
     
  4. Apr 21, 2008 #3
    2-(2000/x^2)=0

    i think
     
  5. Apr 21, 2008 #4
    You think? ... have confidence!!!
     
  6. Apr 21, 2008 #5
    2/1000=x^-2
     
  7. Apr 21, 2008 #6

    exk

    User Avatar

    no, try 2=2000/x^2
     
  8. Apr 21, 2008 #7
    x=square root of .001?
     
  9. Apr 21, 2008 #8
    [tex]x=\sqrt{1000}=\sqrt{10\cdot10^2}=10\sqrt{10}[/tex]
     
  10. Apr 21, 2008 #9
    [tex]x=\sqrt{1000}=\sqrt{10\cdot10^2}=10\sqrt{10}[/tex]

    how did u get that?
     
  11. Apr 21, 2008 #10
    [tex]2=\frac{2000}{x^2}\rightarrow x^2=\frac{2000}{2}\rightarrow x^2=1000[/tex]
     
  12. Apr 21, 2008 #11
    thanks alot. am messed up today!
     
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