Simple optimization problem

1. Apr 21, 2008

physicsed

[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. Apr 21, 2008

rootX

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

3. Apr 21, 2008

physicsed

2-(2000/x^2)=0

i think

4. Apr 21, 2008

rocomath

You think? ... have confidence!!!

5. Apr 21, 2008

physicsed

2/1000=x^-2

6. Apr 21, 2008

exk

no, try 2=2000/x^2

7. Apr 21, 2008

physicsed

x=square root of .001?

8. Apr 21, 2008

rocomath

$$x=\sqrt{1000}=\sqrt{10\cdot10^2}=10\sqrt{10}$$

9. Apr 21, 2008

physicsed

$$x=\sqrt{1000}=\sqrt{10\cdot10^2}=10\sqrt{10}$$

how did u get that?

10. Apr 21, 2008

rocomath

$$2=\frac{2000}{x^2}\rightarrow x^2=\frac{2000}{2}\rightarrow x^2=1000$$

11. Apr 21, 2008

physicsed

thanks alot. am messed up today!