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Simple optimization problem

  • Thread starter physicsed
  • Start date
52
0
[SOLVED] simple optimization problem

1. Homework Statement

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

2. Homework 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?
 

Answers and Replies

351
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
 
52
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2-(2000/x^2)=0

i think
 
1,750
1
52
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2/1000=x^-2
 
exk
119
0
no, try 2=2000/x^2
 
52
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x=square root of .001?
 
1,750
1
[tex]x=\sqrt{1000}=\sqrt{10\cdot10^2}=10\sqrt{10}[/tex]
 
52
0
[tex]x=\sqrt{1000}=\sqrt{10\cdot10^2}=10\sqrt{10}[/tex]

how did u get that?
 
1,750
1
[tex]2=\frac{2000}{x^2}\rightarrow x^2=\frac{2000}{2}\rightarrow x^2=1000[/tex]
 
52
0
thanks alot. am messed up today!
 

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