This document discusses using optimization and math modeling to solve a life problem involving allocating a fixed amount of wire to maximize the total area of a square and circle. It presents a math problem where 4 feet of wire must be used to form both shapes. The math model defines the total area as the sum of the square area and circle area in terms of x and r, with the wire length constraint. Taking the derivative and setting it equal to 0 allows solving for the maximum total area.

1. Life Optimization
Problems
Prersented by : Claire Gui

2. Power & Light Company

3. Math Model

4. Math Problem
Four feet of wire is to be used to
form a square and a circle. How
much of the wire should be
used for the square and how
much should be used for the
circle enclose to maximum total
area?

5. Math Model
A = area of square+area of circle
= x² + πr²
the length of wire is 4 feet
4 = 4x + 2πr
r=
premeter = 4x
circumference=2πr
π
）（ x-12
Area = x² + πr²
22
]
)1(2
[
π
π
x
xA


]48)4[(
1 2
 xxπ
π

6. Find the Maximum area
premeter = 4x
circumference=2πr

7. Using Optimization Problem
Micro level : particles
Life problems :
supply,price...
Marco level : universe