A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides won't require fencing). She has decided to create a rectangular shape for the area, and will use barbed wire to create the enclosure. There are 600 feet of wire available for this project, and she will use all the wire. What is the maximum area that can be enclosed by the fence? (Hint: Use this information to create a quadratic function for the area enclosed by the fence, then find the maximum of the function.)

Question

anonymous · Answer

Let the length of the rectangular pasture be x and breadth be y. 
assume that one side of the length is along the river.So the wire will be used in covering 3 side 
x+2y=600 
Now Area=xy 
=y(600-2y) 
=600y-2y^2 
this is a quadratic in y.Differentiate the function and equate it to 0 in order to find the maximum value. 
y=150 
therefore x=300 
So the maximum area will be A=xy=45000

anonymous · Answer

Oh ok, I get it. So the quadratic equation here is f(x)=-2x^2+600x?

anonymous · Answer

thats correct

anonymous · Answer

Thank you man! Really helps