A rectangular plot of farmland will be bounded on one side by a river, and on the other three sides by a single strand electric fence. With 1900m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

Question

anonymous · Answer

let a be the length and b be the breadth
so. area=A=ab          ........(1)
2a+b=1900
i.e b=1900-2a         .........(2)
sustitute eq one in two
A=a(1900-2a)
A=1900a-2a^2
Now find dA/da
dA/da=1900-4a
For maximum area put dA/da=0
hence 0=1900-4a
a=475m
so b=1900-475=1425m
You will have maximum area in dimentions 475x1475