Another cool optimization problem

[physicsed]

Homework Statement

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

Homework Equations

area = XY

100 = 2x + 2y

y= 100/4x

x(100/4x)

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

1/16x^2 = 0

The Attempt at a Solution

well...
am lost

 

[exk]

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.

 

[physicsed]

2y = 100/2x

y = (100/2x) * .5

 

[exk]

How are you getting from 100=2x+2y to 2y=100/2x?

 

[physicsed]

am trying to solve for y

 

[physicsed]

y = (100/2)-x

 

[exk]

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

So what's the next step.

 

[physicsed]

find the derivates of 50x-x^2
50-2x=0
x=25
100=2(25)+2y

 

[physicsed]

y= 25

 

[exk]

Yep, that's it.

 

[physicsed]

thanks alot. care for one more problem?

 

[Dick]

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.