# math

posted by .

a farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclose?

• math -

3 w + 2 L = 10,000
so
w = (10,000 -2 L)/3

A = w L = (10,000/3)L -(2/3)L^2
we could find the vertex or we could use calculus
first find the vertex
A is 0 when L = 0
A is 0 when (2/3)L =10,000/3
or when L = 5000
so vertex is halfway between
L = 2500
then
w = (10,000 - 5,000) /3 = 5,000/3 = 1667

Now with calculus
dA /dL = w dL/dL + l dw/dL = w + L dw/dL
when dA/dL = 0 we have an extreme
w = -L dw/dL
but w = 10,000/3 - (2/3) L
so
dw/dL = -2/3
so
w = (2/3) L
so
2 w = 10,000/3
w = 5000/3
then L = 10,000/4 = 2,500
which we knew from the parabola anyway

• math -

a farmers wants fence 250 h/a of land,
how much meters are in there?

## Similar Questions

1. ### Math

a farmer wants to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. if the farmer can only afford 1000 yards of fencing, what dimensions …
2. ### Calc 1

A farmer with 700 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
3. ### Math

farmer wants to enclose his pasture which is bordered by a river. If he uses 750 feet of fencing on three sides of the field, what is the largest area he can enclose?
4. ### math

A rancher with 7000 yds of fencing wants to enclose a rectangular field that borders a straight highway and then wants to devide it into two plots with a fence parellel to the highway. If no fence is needed along the highway, what …
5. ### Math

A farmer uses 1034 meters of fencing to enclose a rectangular region and also to subdivide the region into three smaller rectangular regions by placing a fence parallel to one of the sides. Find the demensions that produce the greatest …
6. ### algebra2

A farmer has 600 yards of fence. He will use some of the fence to enclose a rectangular area. He will use the rest divide the area into two congruent rectangles. What is the value of x that results in largest area?
7. ### Math

A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 1600 yards of fencing, what dimensions …
8. ### math

An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible total …
9. ### Precalculus

A farmer with 10000 meters of fencing wants to enclose a rectangular field and divide it into two plots with a fence parallel to the sides. What is the largest area that can be enclosed?
10. ### math

a gardner having 150 meters of fencing materials wishes to enclose a rectangular plot of land and also erect a fence across the land parallel to two of the sides.find the maximum area he can enclose

More Similar Questions