41

CHAPTER – 3

OPTIMUM PLANS FOR MARGINAL FARMERS USING

LINEAR PROGRAMMING MODEL

3.1 INTRODUCTION

Linear Programming (L.P.) is a special class of optimization techniques, where the objectives

and the constraints are all linear functions of decision variables. The first spark for the

phenomenal growth of interest and the practical applications of linear programming problems

came in 1947, when GB.Dantzing formulated the general linear programming problem and

developed the Simplex Method for its solution. It was published for the first time in

[Koopman(1951)].

Linear Programming has been used in agriculture almost since its very inception. Waush

(1961) applied this technique to the problem of minimization of cost of dairy cows. Complete

the farm planning by means of Linear Programming was initiated by Heady and Love (1952).

Boles (1955) has applied Linear Programming in farm management analysis. An extensive

industrial use of L.P. in agricultural farm management analysis has been the field of mixing

with the object of minimizing the cost of feed mix. Barker (1964) conducted a study in the use

of L.P. in making farm management decisions and came to the conclusion that “L.P. can be

value in farmer decision specified alternatives levels of resources use, and the larger the size

of farm, the larger the number of alternatives and greater the likelihood of benefits from L.P.”

In addition to their uses at the micro level, that is cost minimizing the profit maximization of

an individual farm, L.P. techniques have also been applied usefully at the macro level for

solving the problems of agricultural marketing. A major part of the foreign exchange could

have been used for augmenting industrial and other development programmes, until a few

42

years ago, was used up in the import of food grains to feed the ever increasing population of

the country. The agriculture scenario in India until a few years was marked by traditionalism

which resulted low yield and low income. However there have been tremendous

improvements in the areas of farming technology is associated with large investments on

farms due to increase share of inputs like fertilizers, plant protection, chemicals and irrigation

etc. Consequently the weaker sections of farmers have not been benefited from this

technological development in agricultural sector in India.

Farmers in India are generally classified in three categories according to their land holdings

viz. marginal (having area below 1 hectare) , small (having area between to 2 hectare) and

large (having area more than 2 hectare (1974),Singh and Sharma (1987, Bhogal et. Al.

(1988)]. However in some other studies, [Sainy and Singh (1978), Singh and Saudhy (1979)

etc.] farmers having land holding between 2 to 4 hectares are classified as medium farmers

and farmers having land holding above 4 hectare as large farmers. But it is now, by and large

established that behavior pattern of medium and large farmers in terms of production and

resource use in almost alike. The majority of India’s rural population is comprised of marginal

and small farmers. The Government of India and had been giving major emphasis through

rural development programmes to improve the economic condition of this poor section of

rural area and the economic stability and prosperity of nation would to a great extent, depend

upon the performance of these farmers.

Marginal farmers face several constraints in the adoption of improved technology due to

paucity of recourses. “Green Revolution” has increased up to some extent total output and

income of the farmers but the marginal farmers could not gain much from this revolution and

hence the need to investigate in details the ways and means for improving profitability and

productivity for this class of farmers. Moreover, National commission on agriculture in its

43

interim report [India govt. (1973, 1976)] also emphasized the need for scientific studies to be

taken up in various agro climate regions of the country to determine (a) the economic size and

type of livestock enterprises for small and marginal farmers, (b) the possibilities of increasing

the income in different farming systems involving livestock and other components and (c) the

potential of utilization of family labour. The present study is a step in this direction as it

provides optimum farming plans for maximizing the net incomes of the marginal farmer of

Raipur Block in Dehradun District of Uttarakhand. In this chapter L.P. has been used to

develop two different optimum plans one with restriction on livestock enterprises and other

with no restriction on livestock enterprises. A comparative study of these plans with existing

real situation has also been made.

3.2 SOME PROBLEMS OF MARGINAL FARMERS AND NEED FOR

OPTIMIZATION

The farmers in India specially the marginal ones, have inertia not to change their

traditional crop rotations. Besides the farmer’s inertia, some other major

considerations in decision making for optimum farm planning are as under: -

(i) Which crop rotations are to be followed to meet the family

consumption requirement and for market sale?

(ii) How to make best utilization of family labour?

(iii) Which farming system i.e. combination of crops and livestock

enterprises is most suitable?

(iv) How to make the optimum use of scare resources like land and and

Capital?

44

Due to these complex cities of the problem, the decisions of the farmers

regarding the choice of crop rotation and live stock enterprises are far removed

from optimum. Sufficient potential exists for improving agricultural production

and augmenting farm income with proper allocation of existing resources.

Hence, optimum use of land, labour and capital has acquired paramount

importance, particularly in our country, is facing a severe population

explosion.

Linear Programming (L.P.) is a powerful technique to find optimum allocation

of resources. Several studies have been made on farmers of specified regions in

and outside India which provide optimum plans using Linear Programming.

[Kahlon and lohl (1962), Kapur and Kahlopn ,1967), Singh K. (\978), Singh

and Sharma (\988) etc.]. However, hardly any such studies have been

conducted so far in Dehradun, which a district of Uttarakhand having

uniform agroc!imatic conditions. The research facilities in Dehradun district

area not adequate. Consequently the farmers are not aware of latest beneficial

crop planning and other developments in agricultural sector. Therefore, in the

present chapter an attempt has been made to suggest optimum plans to the

marginal farmers belonging to Dehradun District to improve their net returns in

such a way that their traditional system of farming is retained. The main

features of the plans developed are that they cause least change in the

conventional approaches of the marginal farmers.

45

3.3 SAMPLING DESIGN AND DATA

3.3.1 Sampling Design

A list of marginal farmers belonging to Thano, village of Raipur Block of

Dehradun District of Uttarakhand was obtained and a sample- of 50 marginal

framers was selected by using Simple Random Sampling without replacement.

The survey was conducted during the agricultural year 2005.

3.3.2 Preparation of questionnaire and the pilot survey

For the collection of data a questionnaire was prepared and was tested through

pilot survey (in Kheldi Village of Haridwar District, Uttarakhand personal

interview method.) Based on the results of Pilot Survey, suitable modifications

were made in the schedule.' One of the major change, after pilot survey was

the language of the schedule, from English to Hindi. It was felt that was

difficult to explain the questionnaire to the farmers and therefore all the

questions in the schedule were converted into simple Hindi language to make

them understandable to the farmers.

Some new questions were also added for example (i) Questions regarding the

money available with the farmer before starting the cropping in both the

seasons Rabi and Kharif. (ii) Questions regarding minimum and maximum

area restrictions for different crop and (iii) Question related to restriction on

maximum of livestock enterprises. The question regarding the name of the

farmer was deleted because it was observed that farmers hesitate to give actual

information regarding their net income. After incorporating all the

46

improvements based on pilot survey, a final schedule was prepared.

or the sake of convenience the schedule was divided into two parts.

Part - I : In this part information of general nature was collected on the following

points:

(i) Village & Block

(ii) Land holdings

(iii) Cash available with the farmer before growing the crop in both the

seasons.

(iv) Crop rotations followed.

(v) Livestock establishment.

(vi) Labour available in peak periods.

(vii) Minimum and Maximum area restriction on crops.

(viii) Family members.

(ix) Family expenses

(x) Equipments and machines etc. if any.

Part -II: In this part of the schedule, detailed information regarding the crop

grown was obtained. includes mainly the following information:

(i) Total production of crop, its sale price, type of crop by product, it any

etc.

(ii) Operational cost, i.e. the detailed information of human labour, bullock

days, machine/ tractor used during various operations of crop.

(iii) Material costs used in crop growing. which includes cost of seeds,

manure, fertilizer, irrigation and chemicals etc.

47

The data used in this study were collected through personal interview

method from the sample farmers.

3.4 THE LINEAR PROGRAMMING MODEL

3.4.1 Description of the Decision variables included in the L.P. Model

(A) Crop activities and corresponding decision variables: All the

important annual crop rotations followed in the area were taken as crop

activities in the model. The important crop rotations included in the

model were as follows:

1 Bajra - Wheat (H.Y.V.)

2 Maize - Wheat (H. Y. V.)

3 Unused - Wheat (H.Y.V.)

4 Paddy (H.Y.V.) - Wheat (H.Y.V.)

5 Sugarcane (1148)

6 Bajra - Wheat

7 Bajra Urd - Wheat

8 Maize - Wheat

9 Maize + Urd - Wheat

10 Maize + Urd - Wheat + Mustard

11 Paddy (H. V.) - Wheat

12 Paddy (local) - Wheat

13 Sugar cane (768)

48

14 Sugar Cane (Ratoon)

15 Unuscd- Wheat

16 Potato – Unused (Unirrigated)

17 Bajra + Urd-Unused

18 Maize +Arhar (Unirrigated)

19 Jawar + Arhar (Unirrigated)

(H.Y.V. High Yielding Variety)

On the basis of above nineteen crop rotations prevailing in the study area, nineteen decision

variables, (Xl, 1,2, 19), were included in the model where Xi indicates the area (in

hectare) devoted to the ith crop rotation.

was also observed that although there' is a change in traditional ploughing system from

bullock labour to tractor even then there are fanners who still want to keep it with them.

Therefore, one variable, was included in the study. The net return coefficient associated with

this variable was taken as zero, as there is not net return from this activity.

Family labour employment outside and corresponding decision variables:

The following variables were included, indicating family labour employment

outside the family farm on month wise basis, as it was observed that marginal

farmers are allowing family labour to seek employment outside. In order to

observe the employment pattern in each month, the following twelve variables

were included:

X 21: Labour employment in July (in mandsys)

X 22: Labour employment in August (in mandsys)

X 23: Labour employment in September (in mandsys) X 24: Labour

employment in October (in mandsys)

49

X 25: Labour employment in November (in mandsys)

X 26: Labour employment in December (in mandsys)

X Labour employment in January (in mandsys)

X Labour employment in February (in mandsys)

29 Labour employment in March (in mandsys)

30: Labour employment in April (in mandsys)

31: Labour employment in May (in mandsys)

X Labour employment in June (in mandsys)

One the basis of

the collected information, it was observed that the marginal farmers generally

followed mixed farming system, specially crop farming and keeping of milch animals

i.e. dairying. There were different types of milch animals existing in the area and

accordingly the following seven variables were included as live stock activities in the

model.

33

34

35

36

50

36

1jjj XCz

j

20

j

were taken as Rs. 60 each, as it indicates the labour rates per manday,

during the months from July to March. However, during the months April,

May and June it was observed that labour rates were slightly higher and

therefore the values of CJ, for 30, ..... 32 were taken as Rs. 70. the returns

from ivestock enterprises were also calculated, and were included in the

model.

3.6 DESCRIPTION OF CONSTRAINS IN THE MODEL

The constraints considered in the model are only due to limited resources like land,

human labour days for crop production and other activities, working capital, and

managerial constraints in terms of restriction on the area under different crop rotations.

These constraints are explained below:

(a)

51

(b)

(c)

(d) Restriction on number of livestock: on an average it was found that at least one

bullock was maintained by each farmers. Therefore, a provision was made to

maintain the same number in the optimum plans. Restrictions were also imposed

on the number of other livestock i.e. milch animals in the optimum Plan 1. They

were restricted to average maximum number of live stock maintained on the farms.

Similarly the restriction on number of crossbred cows was calculated. It was found

that on the average farmers maintained at the most only 2 milch animals and 1

crossbred cow. The optimum Plan II was developed by relaxing the imposed

restriction on livestock in order to know the potential of income and employment.

(e) Lower and upper area restriction for different crop rotations: In both the

52

optimum plans the lower and upper bound restrictions were imposed on the area

under various crop rotations to make sure that the optimum farming plan do not

have extreme changes in the pattern and level of activities taken on the farms and

the plan be within the adjustable limits or the farmers. The lower limit for different

crops corresponds to family consumption needs on a farm.

3.7 ESTIMATION OF PARAMETERS

order to formulate the model various estimates of parameters were

obtained. As simple Random Sampl ing was used for the selection of farmers

so sample mean (average) is used to estimate the various parameters, like net

returns, land available, cash available, labour mandays etc. in other words to

calculate all the input and output coefficients the average requirements of

various resources per hectare of crop activity and per animal for live stock

activity were calculated and used as estimates of the various parameters of the

model.

3.7.1 Estimation of Net Returns

Net returns from crop activities:

The net return for a crop rotation is defined as:

Net return per hectare for a crop rotation = Gross income from the crop

rotation per hectare – input cost in

crop rotation per hectare

Where Gross income = Value of main product + value of by product ( if any)

Input cost = operation cost + Material cost.

53

An example for calculation: For a farmer having the first crop rotation "Bajra" - Wheat

54

the following information were obtained.

(a) Operational cost = Cost involved (by human labour bullock labour, tractor etc.) during

various operations like ploughing, harrowing, planting, sowing, manunng, fertilizer

application, harvesting, threshing, winnowing, transporting etc. Rs. 3962/-

(b) Material = Cost involving in fertilizer purchasing irrigated charges chemicals, seeds etc.

Rs. 1002/-

(c) Input Cost = Rs . 4964 / -

(d) Gross income = Rs. 29550/ -

Therefore net return per hectare 29560 - 4964 24586/-

Simi the net returns per hectare were calculated for other farmers adopting the same crop rotation

and the estimate of net returns per hectare obtained by taking the average all the values, which

was found to be Rs. 24630/-. The similar procedure was adopted for calculating the other estimates

for net returns per hectare from different crop rotations. explained earlier

(assumed), which gives no cash return from number of bullocks.

(a) Net returns from labour employment in different months: It was observed that the

wages of labour prevailing in that area were Rs. 60 per manday of labour throughout the

year except in the months April, May and June, in which the wages were Rs. 70 per

manday. Therefore the estimates were

C21 = 60, C22 60, C23 60, C24 60. C25 60, C26 60 C27 60.

C28 60, C29 60, C30 70. C31 70, C32 70 .

Here C21 ….. C32 gives net returns per manday of labour (in Rs.) from july to june

respectively.

(b) Net returns from The net returns per animal year were calculated as

follows:

55

Net return Total output value - maintenance costs

The output from a milch animal has been valued at the average price of milk in the locality: The

value of total milk yield given in the year was calculated. The value of Ghee. prepared by milk in the

year was also calculated. By adding these two, total output value i.e. total income was calculated.

The maintenance cost. Involves cost of feed i.e. green fodder, dry fodder, cost of concentrates, cost of

human labour, and expenditure on rope, chain etc.

Net returns were calculated for each fanner maintaining different types of livestock activities. By

taking the average of net returns for a particular animal, the estimates were calculated as given in

table 3.2

Table 3.2 Estimate of Net Returns Livestock Activities

Sno. Activity Net-return/ animal / Year (in Rs.)

1 Cow (Deshi) C33 8505

2 Buffalo (Deshi) C34 19077

3 Buffalo (Murrah) C35 22392

4 (Sahiwal x Jersey) Cross breed cow C36 14220

3.7.2 Estimation of available land

The land available with the farmers was to two types viz. Irrigated and unirrigated.

Information was collected for the available land (of both types) individual farmer and

the estimates were obtained separately by taking averages.

The estimates are as follows:

(i) Estimate of irrigated land available .48 hectare

(ii) Estimate of unirigated land available = .21 hectare

Estimation of Minimum and Maximum Area under Different Crop Rotations:

56

(a) Estimate minimum area under different crop rotations: Keeping in view that every

farmer would prefer to keep some land throughout the agricultural year, for specific crops,

which are required for their family consumption, irrespective of net returns i.e. loss or

profit. A provision was made in the questionnaire to collect information from individual

farmer regarding minimum area required for some crops needed for family consumption. it

was found that farmers want to keep some area under Bajra, Maize and Wheat. Estimates

of minimum area required for the crops Bajra. Maize and Wheat were obtained by

calculating sample means of the respective minimum area crop data. The following are the

estimates:

(i) Estimate of minimum area required under Bajra = .12 hectare

(ii) Estimate of minimum area required under Maize = .10 hectare

(iii) Estimates of minimum area required under wheat = .20 hectare

(b) Estimates of maximum area under different crop rotation:

Generally the Indian farmers have a ·limited risk bearing capacity due to small holdings and

scarcity of other resources. The yield uncertainty arises mainly from its excessive dependence

on nature particularly the weather and the associated calamities. These uncertainties

discourage farmers in growing only one crop on the entire available land, because a serious

crop failure means not only the loss in net returns but also in investments for the next

crop. So, information regarding maximum .~rea limits for different crops was also collected

and the estimates of maximum area limits for different crops prevailing in the area were

obtained by calculating sample means of the respective maximum area crop data. The

following are the estimates: -

(i) Estimate of maximum area under paddy: .16 hectare

57

The major factor which comes in the way

of efficient utilization of available resources is capital. Cash is required in both the seasons

viz. Kharif and Rabi for buying inputs like seeds, manure, fertilizers, water for irrigation etc.

Two questions were included in the questionnaire in order to know the cash available in both

the seasons.

On the basis of sample, following estimates were obtained by taking sample means.

(i) Estimate of cash available in Kharif 2385

(ii) Estimate of cash available in Rabi 4467

(b) Estimation of input under various crops.

While growing crop, cost is involved during various operations like ploughing, harrowing,

fertilizer application, irrigation, harvesting, threshing etc. and are calculated for different

crops, also separately for all the farmers growing that crops, and then average in put cost i.e.

the estimate of input cost required, were obtained. These values are given in the table 3.3.

(ii) Estimate of maximum area under sugar cane: .20 hectare.

(iii) Estimate of maximum area under potato: .02 hectare.

(iv) Estimate of maximum area under arhar : .17 hectare

(v) Estimate of maximum area under urd-: .10. hectare

58

Crop

Rotation

No.

Crop

(Kharif season)

Estimated input

cost in Rs. (per

Hec.)

Crop

(Rabi season)

Estimate input

cost in Rs. (per

hec.)

1 Bajra 2820 Wheat (HYV) 1218

2 Maize 2652 Wheat (HYV) 6876

3 - - Wheat (HYV) 10458

4 Paddy (HYV) 6630 Wheat (HYV) 8274

5 Sugar cane (1148) 3048 Sugar cane

(1148)

5478

6 Bajra 1440 wheat 6612

7 Bajra + Urd 1584 Wheat 6558

8 Maize 1740 Wheat 5382

9 Maize + urd 1872 Wheat 5172

10 Maize + urd 2070 Wheat+

Mustard

5390

11 Paddy (HYV) 2070 Wheat 3990

12 Paddy (Local) 1482 Wheat 3672

13 Sugar cane (768) 2310 Sugar cane

(768)

4992

14 Sugar cane (Ratoon) 2040 Sugar cane

(Ratoon)

3588

15 - - Wheat 6792

16 Potato 3792 - -

17 Bajra + Urd 1182 - -

59

18 Maize + Arhar 1392 - -

19 Jawar + Arhar 1218 - -

3.7.4 Estimate of Available Labour Different Months

On the basis of data collected through of the questionnaire, monthly supply of family

human labour (Male, Female and Child workers), were calculated in terms of

equivalent mandays (rounded off). On the basis of sample data following estimates of

labour available in different months were obtained:

Estimates of Labour available in different months

Months Estimates of

Labour available

(in mandays)

Months Estimates of

Labour available

(in mandays)

July 92 January 85

August 92 February 92

September 92 March 90

October 85 April 92

November 85 May 85

December 85 June 85

60

3.7.5 Estimation of maximum Number of Livestock Activities:

Data were also collected regarding maximum number of stock activities i.e. (Sahiwal x

Jersey) cows and other milch animals, which the fanners can maintain on their farms. By

calculating the sample means of the available data for the two variables i.e. maximum number of

(Sahiwal x Jersey) cows and maximum number of other milch animals the following estimates

(rounded off to nearest integer) were obtained:

(a) Estimate of maximum number of cows (Sahiwal - Jersey) breed = 1

(b) Estimate of maximum number of other milche animals = 2

Information were

collected regarding human labour (in mandays) used in different operations like fertilizer

application, irrigation, sowing, weeding, harvesting, threshing, winnowing and transporting

from farm to home for each crop. Using these data monthwise use of labour was obtained in

growing a particular crop rotation per hectare and by taking the means of month labour used

per hectare for different crop rotations separately, the final estimates of labour used i.e.

average used were obtained. Table 3.4 gives the estimates of month wise labour used/

hectare (rounded off), for different crop rotations,

61

S. Crop Rotation Estimated labour used per hectare (in Ju Au Se Oct No De Ja Feb M Ap Ma Jun

1 Bajra - Wheat 31 47 38 5 29 13 10 10 10 32 13 10 2 Maize - Wheat 27 33 31 3 42 12 11 12 8 33 10 12 3 Unused - Wheat 3 '5 4 1 37 . - 12 11 17 34 12 9

6 38 7 4 Pady (HYV)- 34 28 24 3 24 9 4 4 14 17 5 Sugar cane (1148) 30 17 13 16 30 19 11 29 27 22 13

Bajra - Wheat 22 38 29-- 24 29 23 15 17 6 34 17 11 7 Bajra + Urd-Wheat 27 36 26 27 27 22 17 18 7 31 18 12 8 Maizer-Wheat 17 30 42 26 31 22 18 17 6 32 16 11 9 Maize+U rd-Wheat 26 34 30 27 26 21 18 16 7 37 17 12

Maize+Urd-Wheat 17 7 38 17 11 10 24 39 30 26 27 21 19 11 Paddy (HYV) - 19 24 9 17 34 29 8 9 9 24 8 12 12 Paddy (Local)- 14 30 17 14 37 28 11 10 9 27 6 11 13 Sugar cane (768) 25 17 11 13 27 15 8 30 24 20 10 13 14 Sugar cane 29 14 10 14 25 15 6 16 23 21 17 17 15 Unused - wheat 2 1 3 8 24 19 15 17 6 34 18 11 16 Potato - Unused 28 26 24 9 12 17 27

(unirrigated) 17 Bajra+Urd- unused 25 23 13 20 17

(un irrigated) 17 3 5 21 9 6 18 Maize+Arhar 32 24 12 11 24

9 6 6 19 Jawar+Arhar 33 31 08 11 23 14 6 5

Human labour is also used for the maintenance of livestock. Information were collected from

individual farmer regarding family labour employed in the maintenance of livestock.

Estimates of labour used, (rounded off) month wise were calculated and are presented in

table 3.5.

62

3.8 DEVELOPMENT OF L.P. MODEL

On the basis of estimates of various parameters obtained in the above, section 3.7 (a) to 3.7 (h)

following L.P. Model was formulated, containing 36 decision variables and 27 constraints.

3.8.1 The Objective Function

Our objective is to maximize total farm income of an average farm, which is the representative of all

the farms, in the study area. The objective function is of the following form: -

36

1jjj XCz =

19

1jjj XC +

32

21jjj XC +

36

33jjj XC

= A + B + C , (Say) (As C20 = 0)

In the manner, we observe that, it can be split in to three sub parts where,

Part A = 36

1jjj XCz , gives the value of net returns from crop activities,

Part B = 19

1jjj XC

gives the net return from labor employment

And Part C = , 36

33jjj XC gives net returns from live stock activities.

Thus, the objective is :

Maximize the

+

17+ 18+ + + + + 26 + +

+ + 30 + + +

63

The entire land available with the. farmer was of two types

irrigated and unirrigated and out of 19 crop rotation, it was found that only 4 crop

rotation i.e. and can be applied in un irrigated land. Therefore

following two constraint were introduced.

1 2 3 4 5 6 7 8 9 10 11 12 13

14 15

16 17 18 19

1 6 7 17

2 8 9 10 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15

(iv) Maximum land restriction:

64

Due to uncertainty in production farmers generally want to have maximum area

limit under various crops. The following (5) restrictions were included in the

model.

(1) Upper limit on area under paddy (ha):

X4 + X11 + X12 .16 ………………………… (6)

(2) Upper limit on area under sugar cane (ha):

X5 + X13 +X14 .20 …………………………..(7)

(3) Upper limit on area under potato (ha):

X16 .02 ………………………….(8)

(4) Upper limit on area under Arhar (ha):

X18 + X19 .17 ………………………….(9)

(5) Upper limit on area under Urd (ha):

X7 + X9 + X10 + X17 .10 ………………………….(10)

(B) Labour restrictions:

The total of labour mandays used on family farm and out side employment was

restricted to the maximum family labour available. So one labour constraint was

imposed for each month as under:

(i) Family labour restriction in July (Mandays)

31 X1+27

+

65

Family labour restriction in August (Mandays)

47 X1+33

+ 9

Family labour restriction in September (Mandays)

38X1 + 31

+ 9

Family labour restriction in October (Mandays)

59X1 + 34

+ 13 85

Family labour restriction in November (Mandays)

29X1 + 42

+ 13 85

Family labour restriction in December (Mandays)

13X1 + 12

+ 13

Family labour restriction in January (Mandays)

10 X1 +11

66

+ 13

Family labour restriction in February (Mandays)

10X1 + 12

+ 13

Family labour restriction in March (Mandays)

10X1 + 8

+13

Family labour restriction in April (Mandays)

32X1 + 33

+ 13

Family labour restriction in May (Mandays)

13 X1 + 10

+ 13

Family labour restriction in June (Mandays)

10X1 + 12

+ 13

67

(c) Capital restrictions: -One of the most important resources needed for cropping is capital.

Depending upon the estimates of input capital used in various activities and available capital

in two main different seasons i.e. Kharif and Rabi, the following two capital constraints were

included in the model

2820XI+2652X2+6630X4+3048Xs 1140X6 + 1584 X + 1740 Xg +

1872X9+2070X1o +2078X11 + 1482XI2 +2310X13 + 2040XI4 +3792 XI6 +1182

X 1392 XI8 + 1218X19 2385 .............................. (23)

1218X1 6876X2 + 1 0458X3 +8274X4 5478Xs +6612X6 +6558X7

+5382Xg +5172X9 +5390X1o + 3990X11 + 3672X +4992Xll + 3588XI4

+6792X15 4467 ……………………………... (24)

On the basis of the estimates already obtained regarding

maximum number of milch animals maintained by marginal farmers the following two

constraints were included in the model.

33 34 35

36

These two constraints were included only in Plan I, while in Plan II they were all together

ignored.

68

Inspite of change over from bullock to tractors, each farmer wants to keep at least one

bullock. So the following constraint was included: -

X20 1 ……………………..(27)

Finally all the decision variables were constrained to be nonnegative as none of them can

assume negative value.

Xj 0 , j = 1,2, 3 ……………………….(28)

The above problem is a standard linear programming problem, with 36 decision variables and

27 constraints along with one non - negatively restriction on each variable. It was solved by

MS Excel, using already existing computer program for the solution of a L.P. Problem.

3.9 L.P. PLAN I AND ITS OPTIMUM SOLUTION

The linear programming formulation of L.P. Plan I may be stated as :

Max 36

1jjj XCz =

19

1jjj XC +

32

21jjj XC +

36

33jjj XC

Where 19

1jjj XC

Give the value of net return form crop activities.

32

21jjj XC

Gives the value of net return from labour employment outside.

69

36

33jjj XC

Gives the value of net returns from livestock activities.

Subject to – Constraints (1) to (27) and non- negatively constraint (28).

Constraints (25) and (26) refers to the restriction on live stock activities in accordance with

the existing habits of farmers.

The above L.P.P. was solved by Simplex method and the following optimum solution was

obtained:-

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Optimum Values of the Decision Variables

Decision

Variables

Value Decision Variables Value

Original X1 .021 X28 42.88

X2 .129 X29 43.32

X4 .16 X30 35.10

X13 .20 X31 38.48

X17 .11 X32 39.04

X18 .07 X35 2.00

X20 1.00 Surplus X39 .11

X21 34.67 X40 .11

X22 32.37 Slack X45 .20

X23 38.91 X46 .09

X24 28.80 X48 38.3

X25 26.10 X49 203.9

X26 37.38

X27 40.9

The optimum value of the objective function is

Zopt = Rs. 102326.16

3.9.1 Interpretation of the Optimal solution

For convenience the variance activities in L.P. Plan I are categorized as :-

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(a) Crop Rotation

(b) Labour Employment outside the family farm.

(c) Livestock Enterprises

The optimum net returns of these three categories are presented in the following

tables:

(a) Net returns form crop rotation:-

The net returns of various crop rotations found the optimum plan are presented in

the table 3.6.

Table 3.6 Net returns from various Crop Rotaton Under L.P. Plan I.

Sno Crop Rotation Area return per

ha (in Rs.)

Net return per

ha (in Rs.)

Total Net

Return (in Rs.)

1 Bajra-Wheat(HYV) .021(3.04%) 24630.00 517.23

(3.24%)

2 Maize + Arhar (Unirrigated) .129(18.6%) 25188 3249.25

(20.38%)

3 Paddy (HYV)-Wheat (HYV) .16(23.99%) 24990 3998.4

(25.08%)

4 Sugar cane (768) .20(28.99%) 30240 6048

(37.94%)

5 Maize + Arhar (Unirrigated) .07(10.14%) 12810 896.7

(5.62%)

72

6 Bajra + Urd (Unirrigated) 0.11(12.94%) 11178 1229.58

(7.7%)

Total .69 15939.16

Also,

Unused Irrigated land = Nil

Unused Un Irrigated land = Nil

Table 3.7 reveals that only six out of nineteen crop rotations are beneficial to the

farmers and the whole of the irrigated and un-irrigated land has been fully utilized.

It was found that among the crop rotations the rotation “Sugar cane (768)” is the

most useful as it occupies the maximum (28.99%) of the total cultivated area and

contributes maximum (37.94%) of the total net returns.

(b) Net Returns from Labour employment out side the Family Farms:

The month wise distribution of employment of family labour outside the family

farm and corresponding net returns under L.P. I, are presented in table 3.7.

Table 3.7 : Net returns from Labour employment (outside) Under L.P.Plan I

Month Employment on farm Employment Net return per Total net return

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(in mandays) outside

(in Mandays)

manday of

labour (In Rs.)

(in Rs.)

July 59.6 32.3 60 1938

Aug. 57.3 34.6 60 2076

Sept. 53 38.9 60 2334

Oct. 53.2 28.8 60 1728

Nov. 58.9 26.1 60 1566

Dec. 47.6 37.3 60 2238

Jan 44.1 40.8 60 2448

Feb. 49 42.8 60 2568

March 46.6 43.2 60 2592

April 56.6 35.4 70 2471

May 46.5 38.4 70 2688

June 45.9 39.0 70 2730

Total 27377

It is clear from the table above that man days available for outside employment are ranging from 26.1

to 43.3 and maximum and number of man days are available in the month March. It is concluded that

farmers can earn an average amount of Rs. 27383 per year by proper outside employment of their

family members.

(c) Net Returns from Livestock activities

The optimum number of milch animals and corresponding net returns are

presented in Table 3.8

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Table 3.8 : Net Returns from Livestock activities

Animal bred No. of Animals Net return per animal Total net returns (Rs.)

Buffalo (Murrah) 2 22392.00 44784.00

(Sahiwal- jersey ) Cow 1 14220.00 14220.00

Total 59004.00

It is clear from table above that only two animals viz. Buffalo (Murrah) and (Sahiwal x Jersey) cow

appeared in the optimum solution. The total net returns from these livestock activities comes out to be

Rs. 59004 per year which is too higher as compared to net returns from crop rotation and labour

employment.

Net return under L.P. Plan I, at a Glance:

On the basis of above table 3.6 , 3.7, 3.8 the total farm income under L.P. Plan I is s

ummarized in table given below table 3.9 :

Table 3.9 : Net Return through various source in F.P. Plan I.

Source Net returns % Contribution to total net returns

Through Crop planning 15939.16 15.57

Through Labour employment

outside

27377 26.76

Through keeping of milch

animals

59004 57.67

Total 100.00

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Obviously the maximum contribution to the net return is from keeping of milch animals and the

minimum contribution is through crop planning. Thus dairying is the most profitable for marginal

farmers.

3.10 L.P. PLAN II AND ITS OPTIMUM SOLUTION

As per their existing habits, farmers do not want to keep more than two milch animals. Hence a

restriction on maximum number of milch animals was imposed in L.P. Plan 1. However, the results

of L.P. Plan I indicated that dairying was the most profitable activity for the marginal farmers so it

was felt that the relaxation in this constraint may result in a better plan for the farmers and hence the

motivation for L.P. Plan II with no restriction on livestock enterprises.

The mathematical formulation of L.P. Plan II remains the same as that of L.P. Plan I except for the

two constraints number (25) and (26) which have been all together removed. The optimum solution

of L.P. Plan II using Simplex method was found to be as below: -

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Optimum Values of the Decision Variables

Decision

Variables

Value Decision Variables Value

Original X1 .132 X31 2.6126

X6 .087 X32 3.6731

X8 .087 X35 6.7327

X9 .08 Slack X37 6.7327

X17 .0191 Surplus X43 .31

X20 1.00 X44 .16

X21 7.7107 X45 .16

X22 5.2417 X46 .20

X23 6.4217 X47 .02

X26 1.6514 X48 .17

X27 2.7057 X50 335.7

X28 9.7120 X51 559.1

X29 9.6074

X30 5.9663

The optimum value of the objective function is Zopt = Rs. 151603.75

3.10.1 Interpretation of the Optimum Solution

The optimum net returns under various activities are presented in the following tables:-

(A) Net Returns from Crop Rotations :

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The net returns found in the optimum solution are presented in table 3.10.

Table 3.10 Net returns from various Crop Rotaton Under L.P. Plan II.

Sno Crop Rotation Area in ( ha)

allocated

Net return per

ha (in Rs.)

Total Net

Return (in Rs.)

%

1 Bajra-Wheat(HYV) ..132(6%) 24630.00 325.11

(7.49%)

2 Bajra-Wheat .0867(39.4%) 18300 1586.61

(36.58%)

3 Maize-Wheat .021(9.5%) 21300 447.3

(10.31%)

4 Maize + Urd + wheat .80(36.37%) 22050 1764

(40.77%)

5 Bajra + Urd -Unused

(Unirrigated)

.0191(8.63%) 11178 213.5

(4.93%)

.22 Total 4336.52

Also,

Unused irrigated area = .31 hectare

Unused unirrigated area = .16 hectare

Total unused land = .47 hectare

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Table 3.10 reveals that only 5 crop rotations are beneficial to the farmers. Out of the total land

available with the farmer only 31.89% of the land is utilized. The maximum area (39.4 %) of the

total utilized area is occupied by crop rotation “Bajra –Wheat” . However, the maximum net

return (40.77% ) to the total net return is contributed by the crop rotation “Maize + Urd – Wheat”.

(B) Net returns from Labour Employment outside the family farms:

The month-wise human labour employment outside under L.P. Plan II is given in the table

3.11.

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Table 3.11 : Net Return from Labour Employment outside under L.P.Plan II

Sno. Month Employment on farm

(in mandays)

Employment

outside

(in Mandays)

Net return

per manday

Total net

return (in

Rs.)

1 July 84.2983 7.7017 60 426.10

2 Aug. 86.7583 5.241 60 314.46

3 Sept. 85.5783 6.44 60 386.46

4 Oct. 85.0000 - 60 0.00

5 Nov. 85.0000 - 60 0.00

6 Dec. 83.3486 1.651 60 99.06

7 Jan 82.2943 2.705 60 162.3

8 Feb. 82.2880 9.712 60 582.7

9 March 80.3926 9.607 60 576.4

10 April 86.0337 5.966 70 417.6

11 May 82.3874 2.612 70 182.8

12 June 81.3269 3.673 70 257.11

Total 27377

Above table 3.11 indicates that man days available for outside employment are ranging from 1.65

to 9.71 . It shows the almost all the family labour is utilized on family farms. The maximum

utilization is in the months October and November. It is concluded that utilization of family

labour on farm is more in L.P. Plan II as compared to L.P.Plan I

(C) Net returns from livestock Activities :

80

The optimum number of milch animals and corresponding net returns in L.P.Plan II is as

follows :

Bufallo (Murrah ) : 6.4234 (ie. 6 or 7)

Total net return form milch animals Rs. 143826

Net Returns Under L.P. Plan II at a glance

On the basis of 3.10 and 3.11 total form income under L.P. Plan II can be summarized in table

3.12 given below:

Table 3.12 : Net Return through various source in F.P. Plan II.

Source Net returns Contribution to total net

returns

Through Crop planning 4336.52 2.9%

Through Labour employment

outside

3441.23 2.3%

milch animals 143826 94.8%

Total 151603.75 100.00

Table 3.12 reveals that maximum contribution (94.8%) to the net returns is from keeping of

milch animals and the minimum contribution is through labour employment outside. It clearly

indicate that dairying is really most profitable activity for marginal farmers as it not only

increases the total net returns on family farm but also increase the proper utilization of family

member on farms.

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3.11 FARM INCOME IN THE EXISTING UNPLANNED SITUATION:

Twenty percent of the sample farmers having highest farm income were selected again in

order to know the maximum possible net return under . unplanned situation. Average income

per year was calculated for these farmers and it was found that average maximum farm

income per year was Rs. 54533.

The average net returns from various activities were also calculated for these farmers and are

presented in table 3.13.

Table 3.13 : Net returns from various activities under existing unplanned situation.

Activities Net returns Contribution to total net

returns

Through Crop planning 10653 19.54

Through Labour employment outside 10670 19.6

Milch animals 33210 60.86

Total 54533 100.00

In order to know the income through employment of labour in the existing unplanned

situation, the monthly labour employment out side the family farm, were also observed and

the average pattern of labour employment is presented in table 3.14.

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Table 3.14 : Net Return from Labour Employment outside under L.P.Plan II

Sno. Month Employment out side

(in mandays)

Employment

on farm

(in Mandays)

Net return

per manday

Total net

return (in

Rs.)

1 July 15 77 60 900

2 Aug. 14 78 60 840

3 Sept. 13 71 60 780

4 Oct. 15 70 60 900

5 Nov. 18 67 60 1080

6 Dec. 11 74 60 660

7 Jan 10 75 60 600

8 Feb. 9 83 60 540

9 March 11 79 60 660

10 April 20 72 70 1400

11 May 17 68 70 1190

12 June 16 69 70 1120

Total 10670

The following diagram 3.1 shows the net return of the three activities separately together with

the total net return. In this L.P. Plan II is better than L.P. Plan I as it provides almost total

inside labour which is socially very attractive and increase in net return as compared to L.P.

Plan I is higher.

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3.13 COMPARATIVE STUDY OF L.P. PLAN AND L.P. PLAN II

WITH EXISTING UNPLANNED SITUATION

(A) Comparison with respect to total income

The following diagram 3.2 shows the net returns of the three activities separately, together

with the total net under the existing unplanned situation alongwith two suggested plans. The

L.P.Plan I is better than the present unplanned situation in every respect as it give higher net

returns increase by crop rotation , increase by labour employment out side and increase by

keeping milch animals. The land utilization is also 100%. This is despite of the fact that the

labour employment on farm is lesser in this plan.

L.P.Plan II is even better than L.P.Plan I as it provided almost total inside employment of

family labour which is socially very attractive and yields about 175% increase in net returns as

compared to existing unplanned situation and about 50.% increase in net returns as compared as

L.P. Plan I .However for L.P.Plan II additional funds as required may be arranged through

government sponsored Rural Development Programmes.

(B) Comparison with respect to labour employment on farm:

Result of table 3.7 and 3.11 are presented in the graph of figure 3.3, which represents the

pattern of labour employment on farm in different months under existing unplanned situation

alongwith two suggested plans viz . L.P. Plan I and L.P.Plan II.

It show that family labour employment on farm is almost maximum on L.P. Plan II and L.P.

Plan I. However in existing unplanned situation it is more as compared to L.P. Plan. Thus in

the existing situation farmers are using more family labour on farm and still getting lesser net

returns both from cropping as well as livestock activities. Surely it is nothing but wastage of

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very scare resource. It is, therefore, imperative that the family labour should be employed in

some other productive activity either by seeking more employment out side (as in L.P.Plan I)

or by doing more profitable family business like dairying ( as in L.P.Plan II) where in the

family labour need not go searching for out side employment and remains engaged in their

own family business which is even more profitable than the out side employment both

economically as well as socially.

Finally we may conclude that in marginal farmers having very small holdings cropping

provides the least contribution to the total income and so the poor farmers must pay greater

emphasis on other sources of income may be wage earning through out side employment (as

in L.P.Plan I) or adopting dairying is the most profitable activity but it requires additional

capital for purchase of animals which may be arranged, if funds can’t arranged still with the

available resource of land, labour, capital and animals, there is ample scope for improving lot

of marginal farmers over the existing unplanned situation by resorting to proper planning as

suggested in L.P.Plan I.

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