# CHAPTER 3 OPTIMUM PLANS FOR MARGINAL FARMERS USING LINEAR PROGRAMMING MODEL

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1 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 41

2 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 42

3 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) (iii) How to make best utilization of family labour? 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? 43

4 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. 44

5 3.3 SAMPLING DESIGN AND DATA 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 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 45

6 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) (ii) (iii) Village & Block Land holdings Cash available with the farmer before growing the crop in both the seasons. (iv) (v) (vi) (vii) Crop rotations followed. Livestock establishment. Labour available in peak periods. Minimum and Maximum area restriction on crops. (viii) Family members. (ix) (x) Family expenses 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. 46

7 The data used in this study were collected through personal interview method from the sample farmers. 3.4 THE LINEAR PROGRAMMING MODEL 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) 47

8 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) 48

9 X 25: Labour employment in November (in mandsys) X 26: Labour employment in December (in mandsys) X X Labour employment in January (in mandsys) 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

10 z 36 j 1 C j X j j 20 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 j therefore the values of C J, for 30, 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) 50

11 (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 51

12 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 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. 52

13 An example for calculation: For a farmer having the first crop rotation "Bajra" - Wheat 53

14 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 / - (d) Gross income = Rs / - Therefore net return per hectare /- 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 /-. 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 C 21 = 60, C 22 60, C 23 60, C C 25 60, C C C 28 60, C 29 60, C C 31 70, C Here C 21.. C 32 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: 54

15 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) C Buffalo (Deshi) C Buffalo (Murrah) C (Sahiwal x Jersey) Cross breed cow C 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: 55

16 (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 56

17 (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 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

18 Crop Crop Estimated input Crop Estimate input Rotation (Kharif season) cost in Rs. (per (Rabi season) cost in Rs. (per No. Hec.) hec.) 1 Bajra 2820 Wheat (HYV) Maize 2652 Wheat (HYV) Wheat (HYV) Paddy (HYV) 6630 Wheat (HYV) Sugar cane (1148) 3048 Sugar cane 5478 (1148) 6 Bajra 1440 wheat Bajra + Urd 1584 Wheat Maize 1740 Wheat Maize + urd 1872 Wheat Maize + urd 2070 Wheat Mustard 11 Paddy (HYV) 2070 Wheat Paddy (Local) 1482 Wheat Sugar cane (768) 2310 Sugar cane 4992 (768) 14 Sugar cane (Ratoon) 2040 Sugar cane 3588 (Ratoon) Wheat Potato Bajra + Urd

19 18 Maize + Arhar Jawar + Arhar 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 Months Estimates of Labour available Labour available (in mandays) (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 59

20 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, 60

21 S. Crop Rotation Estimated labour used per hectare (in Ju Au Se Oct No De Ja Feb M Ap Ma Jun 1 Bajra - Wheat Maize - Wheat Unused - Wheat 3 ' Pady (HYV) Sugar cane (1148) Bajra - Wheat Bajra + Urd-Wheat Maizer-Wheat Maize+U rd-wheat Maize+Urd-Wheat Paddy (HYV) Paddy (Local) Sugar cane (768) Sugar cane Unused - wheat Potato - Unused (unirrigated) 17 Bajra+Urd- unused (un irrigated) 18 Maize+Arhar Jawar+Arhar 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

22 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 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 z C X = 19 C X + 32 j j j j j 1 j 1 j 21 C + 36 C j X j j 33 j X j = A + B + C, (Say) (As C 20 = 0) In the manner, we observe that, it can be split in to three sub parts where, Part A = 36 z C X j j, gives the value of net returns from crop activities, j 1 Part B = 19 j 1 C j X j gives the net return from labor employment And Part C =, 36 j 33 C j X j gives net returns from live stock activities. Thus, the objective is : Maximize the

23 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 (iv) Maximum land restriction: 63

24 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): X 4 + X 11 + X (6) (2) Upper limit on area under sugar cane (ha): X 5 + X 13 +X (7) (3) Upper limit on area under potato (ha): X (8) (4) Upper limit on area under Arhar (ha): X 18 + X (9) (5) Upper limit on area under Urd (ha): X 7 + X 9 + X 10 + X (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 X

25 Family labour restriction in August (Mandays) 47 X Family labour restriction in September (Mandays) 38X Family labour restriction in October (Mandays) 59X Family labour restriction in November (Mandays) 29X Family labour restriction in December (Mandays) 13X Family labour restriction in January (Mandays) 10 X

26 + 13 Family labour restriction in February (Mandays) 10X Family labour restriction in March (Mandays) 10X Family labour restriction in April (Mandays) 32X Family labour restriction in May (Mandays) 13 X Family labour restriction in June (Mandays) 10X

27 (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 2820X I +2652X X X s 1140X X Xg X X 1o +2078X X I X X I X I X 1392 X I X (23) 1218X X X X X s +6612X X X g +5172X X 1o X X +4992X ll X I X (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 These two constraints were included only in Plan I, while in Plan II they were all together ignored. 67

28 Inspite of change over from bullock to tractors, each farmer wants to keep at least one bullock. So the following constraint was included: - X (27) Finally all the decision variables were constrained to be nonnegative as none of them can assume negative value. X j 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 z C X = 19 C X + 32 j j j j j 1 j 1 j 21 C X + 36 C X j j j j j 33 Where 19 j 1 C j X j Give the value of net return form crop activities. 32 j 21 C j X j Gives the value of net return from labour employment outside. 68

29 36 j 33 C j X j 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:- 69

30 Optimum Values of the Decision Variables Decision Value Decision Variables Value Variables Original X X X X X 4.16 X X X X X X X X Surplus X X X X Slack X X X X X X X X X The optimum value of the objective function is Zopt = Rs Interpretation of the Optimal solution For convenience the variance activities in L.P. Plan I are categorized as :- 70

31 (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%) (3.24%) 2 Maize + Arhar (Unirrigated).129(18.6%) (20.38%) 3 Paddy (HYV)-Wheat (HYV).16(23.99%) (25.08%) 4 Sugar cane (768).20(28.99%) (37.94%) 5 Maize + Arhar (Unirrigated).07(10.14%) (5.62%) 71

32 6 Bajra + Urd (Unirrigated) 0.11(12.94%) (7.7%) Total 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 72

33 (in mandays) outside manday of (in Rs.) (in Mandays) labour (In Rs.) July Aug Sept Oct Nov Dec Jan Feb March April May June Total 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 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

34 Table 3.8 : Net Returns from Livestock activities Animal bred No. of Animals Net return per animal Total net returns (Rs.) Buffalo (Murrah) (Sahiwal- jersey ) Cow Total 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 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 Through Labour employment outside Through keeping of milch animals Total

35 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 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: - 75

36 Optimum Values of the Decision Variables Decision Value Decision Variables Value Variables Original X X X X X X X 9.08 Slack X X Surplus X X X X X X X X X X X X X X X X X The optimum value of the objective function is Zopt = Rs Interpretation of the Optimum Solution The optimum net returns under various activities are presented in the following tables:- (A) Net Returns from Crop Rotations : 76

37 The net returns found in the optimum solution are presented in table 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%) (7.49%) 2 Bajra-Wheat.0867(39.4%) (36.58%) 3 Maize-Wheat.021(9.5%) (10.31%) 4 Maize + Urd + wheat.80(36.37%) (40.77%) 5 Bajra + Urd -Unused (Unirrigated).0191(8.63%) (4.93%).22 Total Also, Unused irrigated area =.31 hectare Unused unirrigated area =.16 hectare Total unused land =.47 hectare 77

38 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

39 Table 3.11 : Net Return from Labour Employment outside under L.P.Plan II Sno. Month Employment on farm Employment Net return Total net (in mandays) outside per manday return (in (in Mandays) Rs.) 1 July Aug Sept Oct Nov Dec Jan Feb March April May June Total Above table 3.11 indicates that man days available for outside employment are ranging from 1.65 to 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 : 79

40 The optimum number of milch animals and corresponding net returns in L.P.Plan II is as follows : Bufallo (Murrah ) : (ie. 6 or 7) Total net return form milch animals Rs 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 % Through Labour employment % outside milch animals % Total 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. 80

41 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 The average net returns from various activities were also calculated for these farmers and are presented in table Table 3.13 : Net returns from various activities under existing unplanned situation. Activities Net returns Contribution to total net returns Through Crop planning Through Labour employment outside Milch animals Total 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

42 Table 3.14 : Net Return from Labour Employment outside under L.P.Plan II Sno. Month Employment out side Employment Net return Total net (in mandays) on farm per manday return (in (in Mandays) Rs.) 1 July Aug Sept Oct Nov Dec Jan Feb March April May June Total 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. 82

43 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 83

44 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. 84

45 85

46 86

47 87

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