# math

A farmer has 25 yards of fencing to make a pig pen. He is going to use the side of the barn as one of the sides of the fence, so he only needs to fence 3 sides. What should be the dimensions of the fence in order to maximize the area?

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1. length of side parallel to barn ---- y
length of each of the other two sides --- x
y + 2x = 25
y = 25-2x

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

d(area)/dx = -4x + 25 = 0 for a max of area
4x = 25
x = 25/4 , then y = 25 - 25/4 = 25/4

or

from :
area = -2x^2 + 25x , a downwards parabola,
the x of the vertex = -b/(2a) = -25/-4 = 25/4 , as above
y = ...... , same result

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