Posted by **katie** on Tuesday, November 16, 2010 at 9:17pm.

A 100 inch piece of wire is divided into 2 pieces and each piece is bent into a square. How should this be done in order of minimize the sum of the areas of the 2 squares?

a) express the sum of the areas of the squares in terms of the lengths of x and y of the 2 pieces

b) what is the constraint equation relating x and y?

c) does this problem require optimization over anopen or closed interval?

d) solve the optimization problem

- Calc -
**Reiny**, Tuesday, November 16, 2010 at 9:36pm
Let one piece to shape the first square be 4x, then let the other piece be 4y

4x + 4y = 100

x+y = 25

y = 25-x

Sum of areas = x^2 + y^2

= x^2 + (25-x)^2

= 2x^2 - 50x + 625

d(Sum of areas)/dx = 4x - 50

= 0 for a max/min of the sum of the areas

4x = 50

x = 12.5

( I defined the length as 4x instead of x to avoid fractions)

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