Farmer Ed has 5000 meters of fencing and wants to enclose a

Farmer Ed has 5,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed? The largest area that can be enclosed is square meters.

Solution

Dear Student

Thank you for using Chegg !!

Let x be breadth of the rectangular plot as indicated in the snap given in question and 5000-2x is the length

Area of plot is given by

A = (x) (5000-2x)

= 5000x - 2x^2

In order to maximize the area let us differenciate A w.r.t x

dA/dx = 5000 - 4x

if dA/dx =0

5000-4x =0

4x = 5000

x= 1250 meters

again differenciating dA/dx we get

d2A/dx2 = -4

Since double differenciation is negative => x = 1250 corresponds to maximum area.

Maximum area = (1250)(3750)

= 4687500 m^2

Solution