Taraz Kazakh-Turkish boarding school for gifted girls named after
Aysha bibi
“Decision of ecological problem: Optimum
distribution of cattle in pastures.”
Summary
The project “Decision of ecological problem: Optimum distribution of cattle in
pastures” was prepared by Tazhibaeva Aynur and Seitkhanova Asel students of 10th grade
of Taraz Kazakh-Turkish boarding school for gifted girls named after Aysha bibi.
In this project we observe a problem, which investigates decision of one
ecological problem of the agrarian country, namely the correct distribution of
optimum amount of cattle and its arrangement in pastures. This also helps to
preserve ecosystem of this environment. However, it’s important to determine
optimum region of pastures as well and to make the right distribution of each
pasture to preserve ecosystem of the region.
The aim of the project:
The goal of our project is to develop ecologically correct planning of cattle
distribution on pasture in order to use as much as possible definite area of free land
and at the same time to keep conditions at which gramma grass could be
completely restored.
The advantages of the project:
Economic result of the project is cheap and doesn’t’ require a lot of
expenditure for pollution abatement. It’s unnecessary to use expensive materials.
In addition, to make correct planning is not difficult. So, for a person, who hasn’t
got deep knowledge of Mathematics or Economics it is simple and easy to
understand.
Introduction
More than 50 percent of the nations’ population in Middle Asia runs a
domestic agriculture, namely sheep, goats, cows, horses and camels. And they
need to be fed every time. People used to use the whole territory of our land, but in
fact there are not so many pastures in our country with grass that can be eaten by
animals. There is also another problem with reproduction of grass that is used,
because it can not manage to grow up in short time, so cattle eat its roots. That
causes another problem: disappearing of gramma grass, which in general leads to
death of cattle.
This problem may seem not to be so important, but it fact it can be a reason
for a problem much more serious. For example, in 1929-1932 years the whole
territory of Kazakhstan was covered by horrific famine, in which almost 6 millions
of people died. And one of the reasons that caused that disaster was disappearing
of cattle, which in its turn appeared because of the shortage of the gramma grass.
The amount of cattle decreased: sheep- from 18 millions 566 thousands to 1
million 386 thousands heads, horses- from 3 millions 616 thousands to 416
thousands heads, camels – from 1 million 42 thousands to 63 thousands heads.
So we suggest new project, which offers us to plan optimum distribution of
cattle on the pastures. It also includes using of minimum land for maximum cattle
with no harm to ecosystem of environment.
The method
The idea of our project is to start creating pastures with definite amount of
hectares and cattle. We observe 3 situations in which we offer to use some quantity
of pastures, cattle and days during which cattle will devastate grammy grass in
pastures.
Let A be any cattle. In 1 day cattle A finishes 1 hectare of grass. The grass
fully reproduces in 30 days. t is a number of days which it spent in pasture. T is
the amount of days in which the cattle A returns to 1st pasture. n is the number of
pastures. S1, S2…Sn is the area of a pasture n. S1, 2, 3,4 is all area of used pastures.
1st occasion
We have 2 same pastures with 30 hectares in each. Cattle A finishes grass in
pasture 1 during 30 days (as it was said before 1 hectare of grass is eaten per day).
Then cattle A moves to pasture 2. While the 2nd pasture being eaten, the 1st pasture
reproduces So after 30 day the cattle can return to pasture 1 and it will continue in
this way.
n=2
t =30 days
Pasture 1
S1=30 hectares
Pasture 2
S2=30 hectares
T = 30 days
t =30 days
S1=S1+S2
S1=30+30=60 hectares
Where:
S1 ,2 - areas of each pasture
t – amount of days used to finish the grass in each pasture
S1 – area in all used pastures
T – the amount of days in which the cattle A returns to 1st pasture
n – the number of pastures.
2nd occasion
We have 3 same pastures with 15 hectares in each. Cattle A finishes grass in
pasture 1 during 15 days (as it was said before 1 hectare of grass is eaten per day).
Then cattle A moves to pasture 2. After devastating 2nd pasture it moves to pasture
3. During the time that 3rd pasture is being eaten the 1st pasture fully reproduces.
And then cattle A returns to pasture 1. And it will continue in this way.
n=3
t = 15 days
Pasture 1
S1=15 hectares
Pasture 2
S2=15 hectares
t = 15 days
Pasture 3
S3=15 hectares
T = 30 days
t = 15 days
S2=S1+S2+S3
S2=15+15+15=45 hectares
Where:
S1 ,2, 3 - areas of each pasture
t – amount of days used to finish the grass in each pasture
S2 – area in all used pastures
T – the amount of days in which the cattle A returns to 1st pasture
n – the number of pastures.
3rd occasion
We have 4 pastures with different areas. S1 – 20 hectares, S2 – 10 hectares,
S3 – 15 hectares, and S4 – 10 hectares. Cattle A finishes grass in pasture 1 during
20 days, in pasture 2 during 10 days, in pasture 3 during 15 days and in pasture 4 –
10 days.
After devastating 1st pasture cattle moves to pasture 2. The cattle empties it
in 10 days and then goes to 3rd pasture. Because the 1st pasture hadn’t reproduced
yet the cattle moves to 4th pasture. Now when the 1st pasture fully reproduces the
cattle can return there.
n=4
t = 20 days
Pasture 1
S1=20 hectares
T = 35 days
Pasture 2
S2=10
hectares
Pasture 3
S3=15
hectares
Pasture 4
S4=10
hectares
t = 10 days
t = 15 days
t = 10 days
S3=S1+S2+S3+S4
S3=20+10+15+10=55 hectares
Where:
S1 ,2, 3, 4 - areas of each pasture
t – amount of days used to finish the grass in each pasture
S3 – area in all used pastures
T – the amount of days in which the cattle A returns to 1st pasture
n – the number of pastures.
* NOTE: Pay attention on the fact that T=35 days and 5 of them are excess.
Optimum distribution
Assume that we have 1 big pasture with 31 hectare in it. Then we separate
with fences into 31 same mini-pastures with 1 hectare in each. Every day cattle
will devastate 1 pasture (1 hectare) and move to the next one through the gate.
After passing to the next mini-pasture the previous gate closes in order to prevent
the cattle from returning. As soon as finishing 2nd mini-pasture it will move to the
3rd and so on until the 31st mini-pasture becomes empty. By then the 1st minipasture will be fully reproduced and cattle A can return there. So it will continue in
this way.
n=31
n1
n2
n3
……………………………….
t = 1 day t = 1 day t = 1 day
S1=1
hectare
S2=1
hectare
S3=1
hectare
n30
n31
t = 1 day t = 1 day
…………………………………
S30=1
S31=1
hectare hectare
The pass between 31st and 1st mini-pastures
T=30 days
S4=S1+S2+…+S31
S4=1+1+…+1=31 hectares
Where:
S1 ,2,…31 - areas of each pasture
t – amount of days used to finish the grass in each pasture
S4 – area in all used pastures
T – the amount of days in which the cattle A returns to 1st pasture
n – the number of pastures.
It is highly recommended:
To divide the whole area of the pastures (S) to equal parts of land (s) so that
the number that we will get (L) will be equal to 31: L=S/s. The amount of cattle on
this parts of land will be equal to m=k*s. Where m is amount of cattle on this parts
of land (s) and k is amount of cattle which eats 1 hectare of grammy grass in 1 day.
M is whole amount of cattle on whole capture which equals to M=m*L.
Result
At the same amount of cattle (1 cattle) and approximately the same amount
of days we get different areas in all used pastures in each occasion:
S1 =60 hectares
S2 =45 hectares
S3 =55 hectares
S4 =31 hectares
So: 60>55>45>31
S1 >S3 > S2 > S4
*
S4 is the optimum distribution
Conclusion
1.
2.
3.
4.
5.
For the 1st time the optimum distribution of cattle in pastures has
been planed and offered in Kazakhstan.
The economical side of our project doesn’t require much money. It
is cheap and useful.
Easy to understand.
Protecting environment. Saving grass roots from being eaten and
destroyed by animals.
As we compare 3 situations that were showed above with what we
suggest in our project we can say that our idea about optimum
distribution of cattle in pasture is the best way of using minimum
land for maximum cattle. It is in its turn economy of land and grass.