Question

2. Farmer John wishes to fence off a total rectangular area of 1500 square feet using two adjoining pens . How can he do this while minimizing the amount of fencing

Answer 1

Answer:

Then, the perimeter is given by 4x+3y=160.

4x=160−3y

x=40−34y

The area of a rectangle is given by A=L×W, however here we have two rectangles put together, so the total area will be given by A=2×L×W.

A=2(40−34y)y

A=80y−32y2

Now, let's differentiate this function, with respect to y, to find any critical points on the graph.

A'(y)=80−3y

Setting to 0:

0=80−3y

−80=−3y

803=y

x=40−34×803

x=40−20

x=20

Hence, the dimensions that will give the maximum area are 20 by 2623 feet.

A graphical check of the initial function shows that the vertex is at (2623,106623), which represents one of the dimensions that will give the maximum area and the maximum area, respectively.

Hopefully this helps!

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Answer 2

Answer:

Then the perimeter is given by 4×+3y =160 .

4×=160 -3y

x= 40- 34y .

there are of a rectangle is given by A=1×w however here we have two rectangle put together, so the total are will be given by

A=2×l×w

A=2 (40_34y)you

A= 80y -32y2

now let's different this function, whith respect toy to find any critical point on the graph.

A; (c) = 80-3y

seting to 0

0=80-3y

-80= -3y

803 =y

X= 40- 34×803

x=40-20

x =20

hence ,the dimensions that will give the maximum area are 20 by 2623feet.

A graphical check of the initial function shows that the verle x is at (20623, 106623 ) which represents one of the dimension that will give the maximum area and the maximum are respectively .