SOLUTION: I decide to take up alpaca farming. I will build an alpaca pen next to my house. ( Since it is next to my house, I don't need any fencing on the side where my house is. My house is

Question 762364: I decide to take up alpaca farming. I will build an alpaca pen next to my house. ( Since it is next to my house, I don't need any fencing on the side where my house is. My house is huge, so I don't have to worry about that side being too short.) I have 800 feet of fencing. What is the most area I can give my alpacas? (The fence can be any shape)
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Use x ft for breadth.
Length = 800 - 2x
Area = Breadth * Length
Area = x(800 - 2x)
Area(x) = 800x - 2x^2
Differentiate
Area'(x)= 800 - 4x
Area'(x) = 0
800 - 4x = 0
4x = 800
x = 200
Check gradient on either side of 200
So maximum occurs when x = 200
So breadth = 200ft
Length = 400ft
Maximum area = 800(200) - 2(800)^2
= 80000ft^2
Hope this helps.
:-)

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