Z=12.1+29i
What is the real part of z?
What is the imaginary part of z?

x = 125 ft and y = 250/3 ft

Step-by-step explanation:

Let assume that,

x be the length of the northern part of the fence (parallel to the north wall)

y be the length of the western and eastern pieces of the fence

As well as farmer has $4000 to spend hence we can write,

8x + 8y + 4y = 4000

8x + 12y = 4000

Hence we can say that,

from the above equation we can write

We know that area

A=xy.

we can write

equating it 0 we get

Also,

which is less than zero.

we can see that A''(x) is always less than 0 hence using second derivative test we can say that x = 125 is a maximum point.

now, solving for y we get  

Hence we can say that dimensions for the plot that would enclose the most area is,

x = 125 ft and y = 250/3 ft