Another cool optimization problem

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Homework Help Overview

The problem involves finding the dimensions of a rectangle with a fixed perimeter of 100 meters that maximizes the area. The subject area pertains to optimization in geometry.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss algebraic manipulations related to the perimeter equation and its implications for the area. There are attempts to express one variable in terms of another and to derive relationships between the dimensions. Some participants question the correctness of specific algebraic steps and suggest reconsideration of earlier calculations.

Discussion Status

The discussion includes various attempts to derive the dimensions, with some participants providing guidance on algebraic accuracy. There is a progression towards finding critical points, but no explicit consensus on the final solution has been reached.

Contextual Notes

Participants are navigating through algebraic expressions and derivatives, with some indicating confusion over earlier steps. The problem is framed within the constraints of a homework assignment, which may influence the level of detail and rigor in the discussion.

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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
 
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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.
 
2y = 100/2x

y = (100/2x) * .5
 
How are you getting from 100=2x+2y to 2y=100/2x?
 
am trying to solve for y
 
y = (100/2)-x
 
Ok that's better (100/2=50).

So what's the next step.
 
find the derivates of 50x-x^2
50-2x=0
x=25
100=2(25)+2y
 
y= 25
 
  • #10
Yep, that's it.
 
  • #11
thanks a lot. care for one more problem?
 
  • #12
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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