A farmer with 5000 feet of fencing wants to enclose a rectangular field and then divide it into two plots by adding a fence in the middle parallel to one of the sides. Using the function A(x) , analytically find the WIDTH of the field that would maximize its area. (Round your answer to the nearest whole number)

The required width of the field that would maximize the area is = 1250  feet

Step-by-step explanation:

Given that:

The total fencing length = 5000 ft

Let consider w to be the width and L to be the length.

Then; the perimeter of the rectangular field by assuming a parallel direction is:

P = 3L + 2w

⇒ 3L + 2w = 5000

3L = 5000 - 2w

Recall that:

The area of the rectangle = L×w

Taking the differentiation of both sides with respect to t; we have:

Then; we set A'(w) to be equal to zero;

So;

5000  = 4w

w = 5000/4

w = 1250

Thus; the required width of the field that would maximize the area is = 1250  feet

Also, the length can now be :

L = (5000 -2500)/3

L = 2500/3 feet

Suppose, the farmer divides the plot parallel to the width; Then  2500/3 feet = 833.33 feet and the length L = 1250 feet.

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