Expert: Paul Klarreich - 10/29/2008

Question
Two sides of fencing are needed to enclose a rectangular area at the corner  of a room. If 20 ft of fencing is provided, find the area of he largest possible rectangle.

Answer
Questioner:   Samantha
Category:  Calculus
Private:  No
 
Subject:  word problems (technology)
Question:  Two sides of fencing are needed to enclose a rectangular area at the corner  of a room. If 20 ft of fencing is provided, find the area of he largest possible rectangle.
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Hi, Sam,

If this is your first time doing a Maximum-minimum problem, here is the scheme.

1. Identify the variables in the problem -- the things that change.  Give them names.

2. Find the one that is to be 'optimized'.  Write it as a function of the other variables.

3. If it is a function of more than one, use the other conditions (constraints) to eliminate all but one.

4. Differentiate, set that = 0, solve for your 'stationary' point.

5. Consider whether it is a maximum, minimum, or neither.  Check the logical endpoints, too.

6. Answer whatever other questions are asked.
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Variables:

x = first side of the rectangle
y = second side
A = area of rectangle

Relation:

A = xy

Constraint:  x + y = 20
Solve:   y = 20 - x

A = x(20 - x)
A = 20x - x^2

You can finish it up from here.