Question

Farmer Ed has 550 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, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

Answer 1

let width of the rectangular plot be x meters

then total of widths = 2x 
and the length would be (550 - 2x) meters.

so the area = x(550 - 2x)  = 550x - 2x^2

to find the maximum are find the derivative and equate to zero:-

f'(x) =  550 - 4x = 0
x = 550/4 =  137.5 meters = width

length = 550 - 2(137.5) = 275

Maximum area  is when width = 137.5m and length = 275m

Answer 2

For the maximum area the length is 275 meters and width is 137.5 meters.

Step-by-step explanation:

Given information:

Farmer Ed has 550 meters of fencing

According to the question:

The total width $=2x$

The total length $=550-2x$

So, the area:

$A=x(550-2x)\\A=550x-2x^2$

For the maximum values find the derivative and equate with zero.

$A'=550-4x$

Now,

$550-4x=0\\x=(550/4)\\x=137.5\;\text{m}$

The width is 137.5 meters.

Now, the length $= 550-2\times 137.5$

$L=275 \; \text{m}$

Hence,

For the maximum area the length is 275 meters and width is 137.5 meters.

For more information visit:

https://brainly.com/question/25120629?referrer=searchResults