Posted by **kayla** on Sunday, October 26, 2008 at 8:48pm.

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 -
**Damon**, Sunday, October 26, 2008 at 9:07pm
3 w + 2 L = 10,000

so

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

A = w L = (10,000/3)L -(2/3)L^2

that is a parabola (quadratic)

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 -
**dudu**, Saturday, October 17, 2015 at 11:18am
a farmers wants fence 250 h/a of land,

how much meters are in there?

## Answer this Question

## Related Questions

- Precalculus - A farmer with 10000 meters of fencing wants to enclose a ...
- Math - a farmer wants to put a fence around a rectangular field and then divide ...
- Math - A farmer wishes to put a fence around a rectangular field and then divide...
- math - A rancher with 7000 yds of fencing wants to enclose a rectangular field ...
- algebra2 - A farmer has 600 yards of fence. He will use some of the fence to ...
- Math - A farmer uses 1034 meters of fencing to enclose a rectangular region and ...
- math - An ostrich farmer wants to enclose a rectangular area and then divide it ...
- area and perimeter - a farmer wishes to build a fence around a rectangular field...
- Math - 1. A gardener has 140 feet of fencing to fence in a rectangular vegetable...
- Calc 1 - A farmer with 700 ft of fencing wants to enclose a rectangular area and...

More Related Questions