Homework Help: Another cool optimization problem

physicsed · Apr 21, 2008

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

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

2. Relevant equations

area = XY

100 = 2x + 2y

y= 100/4x

x(100/4x)

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

1/16x^2 = 0
3. The attempt at a solution

well........
am lost

exk · Apr 21, 2008

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 · Apr 21, 2008

2y = 100/2x

y = (100/2x) * .5

exk · Apr 21, 2008

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

physicsed · Apr 21, 2008

am trying to solve for y

physicsed · Apr 21, 2008

y = (100/2)-x

exk · Apr 21, 2008

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

So what's the next step.

physicsed · Apr 21, 2008

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

physicsed · Apr 21, 2008

y= 25

exk · Apr 21, 2008

Yep, that's it.

physicsed · Apr 21, 2008

thanks alot. care for one more problem?

Dick · Apr 21, 2008

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.