Another cool optimization problem

  • Thread starter physicsed
  • Start date
  • #1
physicsed
52
0

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
 

Answers and Replies

  • #2
exk
119
0
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.
 
  • #3
physicsed
52
0
2y = 100/2x

y = (100/2x) * .5
 
  • #4
exk
119
0
How are you getting from 100=2x+2y to 2y=100/2x?
 
  • #5
physicsed
52
0
am trying to solve for y
 
  • #6
physicsed
52
0
y = (100/2)-x
 
  • #7
exk
119
0
Ok that's better (100/2=50).

So what's the next step.
 
  • #8
physicsed
52
0
find the derivates of 50x-x^2
50-2x=0
x=25
100=2(25)+2y
 
  • #9
physicsed
52
0
y= 25
 
  • #10
exk
119
0
Yep, that's it.
 
  • #11
physicsed
52
0
thanks alot. care for one more problem?
 
  • #12
Dick
Science Advisor
Homework Helper
26,263
621
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.
 

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