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LenKa [72]
3 years ago
12

Farmer Ed has 300meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fenc

e 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?
Width
Length
Largest area:

Mathematics
2 answers:
babunello [35]3 years ago
8 0
L+2w=300

A=(w)(-2w+320)
A=-2w^2 +320w

A=-2(w^2 - 160w)
A=-2(w^2 - 160w+6400) +12800

A=-2(w-80)^2 +12800

The max area is 12800 m squared.

The width is 80 m and the length is 160m.
yarga [219]3 years ago
4 0

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the width is W.

Suppose the length is L.

Total fence is given as 300, so

L+W+W=300

L+2W=300......................(1)

Area=Length*Width

Area=L*W

Plugging the value of L from equation (1)

Area=(300-2W)*W

Area=300W-2W^2

For Area to be maximized, derivative of area should be equal to zero.

Means :

\frac{d}{dW}Area= 300-4W = 0

So, So, W Width = \frac{300}{4}=75

So, L Length=300-2*75=150

So, Largest area= 75*150=11250   :    Answer

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