# Optimization

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A wire 10 feet long is to be cut into two pieces, each of which is to formed into a square. What is the largest possible total area of the two squares? What is the smallest possible total area?

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:57 pm ad1c9bdddfhttps://brainmass.com/math/optimization/optimization-total-area-squares-18262

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Let 2 pieces be x , 10-x.

Total Area = x^2 + (10-x)^2

A = X^2 + 100 + X^2 -20X

dA/dx = 4x - 20.

d2A/d2x ( second derivative) = 4x. Since d2A/d2x >0 , dA/dx = 0 will give the min area.

putting dA/dx = 0 we have 4x = 20

or x = 5.So each side will be 5/4 = 1.25

A = 1.25^2 + 1.25^2 = 3.125 sq units.

Largest possible total area will occur at 10 , 0 of the respective pieces. The total area will be 6.25...( Not in order to maximize the total area of 2 squares , you will need to minimize the length of 1 side which will be 0)

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:57 pm ad1c9bdddf>https://brainmass.com/math/optimization/optimization-total-area-squares-18262