Optimizing Rectangle Dimensions for Area 1000m^2: A Simple Solution

[physicsed]

[SOLVED] simple optimization problem

Homework Statement

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

Homework Equations

perimeter = 2x + 2y

area = xy

1000 = xy

y= 1000/x

perimeter = 2x + 2(1000/x)

The Attempt at a Solution

am stuck

any help from anybody?

 

[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

 

[physicsed]

2-(2000/x^2)=0

i think

 

[rocomath]

2-(2000/x^2)=0

i think

You think? ... have confidence!

 

[physicsed]

2/1000=x^-2

 

[exk]

no, try 2=2000/x^2

 

[physicsed]

x=square root of .001?

 

[rocomath]

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

 

[physicsed]

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

how did u get that?

 

[rocomath]

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

 

[physicsed]

thanks a lot. am messed up today!