ReseaRch PaPeR Journal of Agricultural and Marine Sciences Vol. 22 (1): 27-35 DOI: 10.24200/jams.vol22iss1pp27-35 Received 5 Jun 2016 Accepted 19 Oct 2016 Agricultural resources management through a linear programming approach: A case study on productivity optimization of crop-livestock farming integration Hemanatha, P. W. Jayasuriya1* and Romy Das2 *1 Hemanatha P.W. Jayasuriya ( ) Sultan Qaboos University, Col- lege of Agricultural and Marine Sciences, Dpt. of Soils, Water and Agri- cultural Engineering, Box 34, Al-Khod 123, Sultanate of Oman. Email: hemjay@squ.edu.om. 2Agricultural Systems and Engineering Program, Asian Institute of Technology, Klong Luang, Pathumthani 12120, Thai- land. Introduction The diverse climatic conditions of Nepal has en-abled its people to practice various forms of agri-cultural activities. Farming takes place from the Terai region to the permanently cultivated land above 4000 msl (Schroeder, 1985). At higher altitude, livestock plays the most prominent role in the livelihood and people are mostly pastoralist, whereas in fertile plains, the emphasis is on crop production. In the broad band between high hills and lower mountains area, farmers mostly rely on the century’s old tradition of integrated and diversified mixed crop-livestock farming (Sumberg, 2003; Bell and Moor, 2012). Crop-livestock integration is thus the established characteristics of the hills of Ne- pal. The role of livestock as nutrient recyclers, source of income and draft power obligates farmers to keep large number of livestock leading to high livestock population in the country. Mid hilly region of the country has ap- proximately two third of the country’s livestock popu- lation. Livestock density in Nepal is the highest among South Asian countries. It has been estimated to be 6.52/ ha, which is higher than 3.99 ha, the density in Bangla- desh, where similar climatic and economic conditions exists (FAO, 1990). Excessive grazing on natural forests due to high live- stock population in the hills has resulted into severe deterioration in the growth of shrubs and trees. The ground cover to limit soil erosion is either at a minimum or has vanished. The higher livestock population is not only a pressure on the resources but has also negative impact on the productivity (Anderson, 1997; Bell and Moor, 2012). The majority of the livestock in the hill dis- tricts of Nepal suffers from low nutrition. Even though the animals are of high genetic potential, poor nutrition negatively affects production (Regmi 1992). The mid hills of Nepal have tremendous potential for dairy pro- duction, but its productivity remains vulnerable due to diminishing availability of feed resources and growing number of unproductive animals. إدارة املوارد الزراعية من خالل الربامج اخلطية: حالة دراسية للتكامل الزراعي يف حتسني إنتاج احملاصيل والثروة احليوانية مهاناثا جاياسوريا1* ور. داس2 Abstract. The crop-livestock integrated farming system practiced in most developing countries depends to a greater extent on the ecosystem as a whole. The importance of animals as an agent of nutrient recycle, sources of rural energy in terms of draft power and fuel as well as major contributor of the farm economy, has resulted into increased population of ruminant stock in these regions creating threats to the sustainability and productivity of land resources. This case- study research attempted to formulate optimum herd size compatible to different resource holding farm categories within the sub watershed in mid hills region of Nepal. The research was conducted by classified data collection in Nepal and analysis using Linear Programming (LP) techniques. The LP analysis revealed that the farmers of large, medium and small categories of farms can optimize their livestock holding with combination of 3 Livestock Units (LU) buffaloes and 4 LU goats, 2 LU buffaloes and 4 LU goats and 1 LU buffaloes and 4.4 LU goats with maximum return to the farm family without exerting pressure on the fragile natural resources. Keywords: Livestock Unit; land Resources; optimum herd size; total digestive nutrient supply امللخــص: يعتمــد التكامــل الزراعــي يف الــدول الناميــة بشــكل عــام علــى النظــام البيئــي، إن للثــروة احليوانيــة أمهيــة كبــرة يف تدويــر مغذيــات الرتبــة وإنتــاج الطاقــة وكذلــك إســهامها يف حتســن دخــل املزارعــن، ممــا أدى إىل تزايــد أعدادهــا والــذي قــد يشــكل ضغــط مباشــر علــى املــوارد الطبيعيــة. أن هــذا البحــث حيــدد األعــداد التوافقيــة للثــروة احليوانيــة للوصــول إىل اســتدامة بيئيــة ملنطقــة النيبــال باســتخدام الربامــج اخلطيــة. أظهــرت النتائــج بــأن أصحــاب املــزارع الكبــرة عليهــم اختــاذ 3 وحــدات حيوانيــة مــن اجلامــوس و4 وحــدات مــن املاعــز. يف حــن أن املزارعــن املتوســطن عليهــم اختــاذ وحدتــن مــن اجلامــوس و4 وحــدات مــن املاعــز. أمــا يف املــزارع الصغــرة فعليهــم اختــاذ وحــدة واحــدة مــن اجلامــوس و 4.4 وحــدات مــن املاعــز، حيــث أن هــذا التقســيم ســوف يقلــل الضغــط علــى املــوارد الكلمات املفتاحية: وحدة الثروة احليوانية، موارد األراضي، إمجايل اجلهاز اهلضمي للعناصر الغذائية 28 SQU Journal of Agricultural and Marine Sciences, 2017, Volume 22, Issue 1 Agricultural resources management trough linear programming High livestock population pressure on the natural re- source base as well as on agricultural land is the result of farmers’ poor decisive ability regarding herd size (Price and Hacker, 2009; Bell and Moor, 2012). Rural farmers are mostly confronted with the problem of properly al- locating scarce land and labor resources in a crop and livestock mix farming system (Minh et al. 2007). Reap- ing maximum benefits from available resources necessi- tates proper farm planning to utilize the resources more effectively for crop and livestock production without ex- erting additional pressure on natural resources (Millar and Badgery, 2009). Efficient farm planning regarding livestock holding will further contribute to the economic and sustainable development of the watershed (Agrawal and Heady, 1972; Beneke and Winterboer, 1973; Igwe et al., 2011; Andreea and Adrian, 2012). Although an assessment of carrying capacity in terms of livestock unit is a useful tool for planning as well as policy formulation, it is unable to infer directly the num- ber and the composition of livestock in the farmers’ household (Robertson et al., 2009; Govindrao and Ka- beer, 2011). In fact, livestock rearing not only depends upon the feed available but also on the labor availability because livestock rearing is labor intensive. In this con- text, it is important to formulate the optimum livestock number based on the available resources to the farmers. Tulachan (1989) signified the importance of livestock to enhance the farm income of the rural farmers with the recommendation of various herd size suitable for dif- ferent farm categories. Minh et al., (2007) showed the feasibility of optimizing the crop-livestock integration with an additional component of crop-residue-dung compost fertilizer use. Similarly, Regmi (1992) carried out an economic analysis of the farming system and for- mulated optimum farm plan with equal focus on crop and livestock as enterprises. But both of these studies were conducted in terai and did not represent the condi- tions of mid-hills where the livestock raising contributes significantly to the farm economy. Therefore, this study attempted to formulate the optimum livestock number and its composition, which gives high income to farm family with variable resources, using LP technique. Methodology Site election The study was conducted in Kumpur subwatershed of Dhading district. The watershed covers an area of 66.2 ha, which occupies 3.45% of the total area of the dis- trict. It comprises Kumpur village development com- mittee completely, Sunaula Bazaar and Kalleri partially. The sub watershed constitutes four micro-watersheds covering major tributaries as Adam, Bijuli, Sakura and Thopal Khola of Trishuli River. The elevation within Kumpur sub watershed varies approximately from 446 m near the Trishuli River to approximately 1570 m at the north-eastern corner of the study area. Due to variation in the altitude, a wide range of farming systems can be found even within small sub watershed. Data Collection The outcome of the research is based on primary as well as secondary data collected in Kumpur Sub watershed of Dhading district. The methods of primary data collec- tion were household survey, group discussion and field observation. Similarly, secondary data were collected from annual reports of District Livestock Service Centre, District Soil Conservation Office, District Forest Office, Locally based NGOs and VDC profile. Similarly, pub- lications of International Centre for Integrated Moun- tain Development, articles from International journals and textbooks served as important sources of secondary data. Collected data were analyzed using SPSS (Statis- tical Package of Social Science). Farm plans for three categories of farmers were formulated using linear pro- gramming tools. Data Analysis The linear programming (LP) technique Farmers in hilly region of the country possess very limit- ed resources particularly land, labor and capital. In case of poor resources holding at their own, as well as dwin- dling supply from common pool resources, it is essen- tial to estimate the best combination of available farm resources to maximize the net farm income. The over- all goal of farmers to maximize the farm income with optimum resource allocation allows the use of the LP technique as an appropriate decision making tool in the analysis (Agrawal and Heady, 1972; Beneke and Win- terboer, 1973; Hillier and Liberman, 2001; Minh et al., 2007; Soltani et al., 2011; Govindrao and Kabeer, 2011). Using the shadow prices and sensitivity analysis, ranking of livestock components was done allowing farmers to select the best among several options considering the sociological and economical factors. Mathematically, a linear programming (LP) model can be expressed as follows: Table 1. Farm categorization of the sampled households Farm categories Land holding No. of farm household Small Farm <0.5 ha 58 Medium Farm 0.5- <1 ha 57 Large Farm >1 ha 45 29Research Article Jayasuriya and Das Z max = C i X i i=1 j ∑ (1) subjected to Resources constraints a ij X i ≤b j j=1 m ∑ i=1 n ∑ (2) and Non-negative constraints X i ≥0 (3) where Z = The objective function x j = The level of the jth decision variable c j = Gross margin of unit of the jth activity a ij = The quantity of the ith resource required to produce 1 unit of jth activity m= The number of resources m= The number of possible activities b i = The amount of the ith resource available i =1,2,…m; j =1,2,…n Farm classification Farmers of the study area differed in resource availabili- ties. Resource holding in terms of land, family labor and livestock number were the main basis for farms catego- rization for the LP analysis. However, land holding size served as a major criterion for farm categorization in the model. Livestock Master Plan (1993) also categorized the farm families into large, medium and small farm based on their land holding size. Farmers of the study area were also classified into three groups based on the above criteria. The total 160 sample households were categorized into three groups as given below. The average value of resources such as land, labor, nutrient availability and livestock holdings of sampled farm household were used to construct a representative of three farm categories and linear programming model was run for each representatives farms. Assumptions made in LP Model (1) Crop residues or crop by-product used as main sources of animal feeds for livestock production. The use of crop residue, such as rice straw, maize stover was con- sidered as transfer activities in the integrated farming system. Rice straw was produced in the winter season and stored as feed for rest of the year. Crop residue, as feed sources were considered without their opportunity cost in the model. Similarly, manure production from livestock was considered to be used in the crop produc- tion as Farm Yard Manure (FYM). (2) Return from the bullock was calculated based on the number of days, they are placed for work. Since their use was seasonal, it was assumed that a pair of bullock is used approximately for 180 days in cropping activities. Tulachan (1989) adopted the same method to calculate the return from the draft power use of bullock. (3) Family labor and use of own bullock was consid- ered without their labor cost. For crop production, cost of hired labor was included. However, it was assumed that livestock production is entirely performed through family labor. Returns received from the linear program- ming solution were return to farm labor, family owned bullock and land. Capital cost of each type of livestock in the model was considered using market price and cur- rent interest rates. (4) The main economic animals considered for the models were milking buffaloes, milking cows, draft bull- ocks and goats. The model only considered adult ani- mals which gives economic return. (5) Livestock were assumed to be raised with two dif- ferent feeding management systems. The existing farm plan had taken into account maintenance ration only whereas improved feeding with maintenance and pro- duction rations was considered in the improved farm plan. Decision Variables Used in Linear Programming Model A. Cropping activities Rice and maize were the major cereal crops used as sta- ple food in the study area. Additionally, these were the major sources of crop residues for livestock feed. There- fore, these two crops had been taken as only cropping activities in the model. Production cost per unit was de- ducted from the per unit output value of each cropping activities to get the gross return. B. Livestock enterprises Each type of livestock unit (LU) was considered as a sep- arate activity in the model. Balancing the livestock car- rying capacity (=LU) for each type of livestock, based on TDN requirement, 4 goats were considered as one LU. Since the main objective of the model was to determine the optimum stocking for each farm categories, the num- ber and type of livestock was selected based on available feed resources. Milk production was considered as a major output from cattle and buffaloes. Similarly, draft power use during working periods was considered for the calculation of return from bullock. Return from goat indicated the economic value of meat produced per year. Return from livestock activities was estimated without including the cost of feeds except concentrate. Due to improved feeding, comparatively higher return from buffalo milk production was considered in improved farms plans than the existing plan. C. Fodder plantation Grazing a large flock of goats was difficult under the community sanction of common pool resources in the study area. Moreover, considering the negative effects of the browsing nature of goats on vegetation cover, in- creased number of goats might require increased farm 30 SQU Journal of Agricultural and Marine Sciences, 2017, Volume 22, Issue 1 Agricultural resources management trough linear programming fodder production. Therefore, to minimize the depen- dency on external sources, certain proportion of upland area was considered under fodder tree plantation in all improved farm plans so that stall-feeding of large num- ber of goats can be possible and grazing in common pool resources can be minimized. Since fodder tree occupies certain area under cultivated land, it was considered as a separate activity in the improved farm model. The economic return from fodder tree was calculated with respect to the Total Digestive Nutrient (TDN) value of crop residue. Farm resources and constraints used in LP model A farmer has to take decisions regarding cropping and livestock activities within the boundary of resources available to the farm household. The major resources that a farmer owns are the land, family labor and the capital. These resources are limited for the family there- fore, they demand efficient use. The resources consid- ered in the model are discussed as follows. A. Land resources Land is a scarce resource for the hill farmers of Nepal. Efficient allocation of land is an important factor to be considered in increasing whole farm income. Table  2 presents the land holding of three farm categories. The cultivated land holding was categorized into upland (unirrigated land) and lowland (irrigated land) in each farm category. Rice is grown in the irrigated land there- fore the total available irrigated land was considered as land constraints under rice cultivation. Since there was hardly any option for further increasing the landhold- ing and land type of the farm household, no attempt was made to increase land area under rice and maize in the model. Maize is usually grown in the upland of the area; therefore, bari land (unirrigated land) was taken as con- straints for the area under maize. Fodder trees are grown on the riser and bunds and occupy a certain area of the bari land. Fodder trees are rarely cultivated in khet land due to its shading effect on the crop yield. According to LRMP (1986), about 17.4% of gross cultivated area in Kavrepalanchowk district of Nepal is under riser and bunds. The same figure was assumed in the study area as well. Therefore, the upland area with same figure was allocated under the fodder tree as an equality constraint in the improved farm model. B. Labor resources Labor is the most important resource for crop as well as livestock activities. Cropping activities are seasonal Table 2. Cultivated land holding of farm categories. Farm category Total land holding (ha) Upland holding (ha) Lowland holding (ha) Large Farm (n=45) 1.75 1.25 0.5 Medium arm (n=57) 0.8 0.52 0.28 Small Farm (n=58) 0.43 0.26 0.17 Source: Household survey, Primary data Table 3. Cultivated land holding of farm categories. Age Category Heads Labor Equivalent Estimated LD/month LD/Month in farming LD/year for Labor hours avail- able for farming Large Farm <0-15yrs 2.42 0.5 15 3 72 576 16-59 yrs 3.23 1 30 25 900 7200 >60yrs 0.44 0.5 4 19.2 153.6 Total 7929 Medium Farm <0-15yrs 2.47 0.5 15 3 72 576 16-59 yrs 2.86 1 30 25 900 7200 >60yrs 0.37 0.5 15 4 14.4 115.2 Total 7891 Small Farm <0-15yrs 1.81 0.5 15 3 72 576 16-59 yrs 3.02 1 30 25 900 7200 >60yrs 0.28 0.5 15 4 9.6 76.8 Total 7852 Source: Household survey, primary data 31Research Article Jayasuriya and Das and required to be performed within a specified period of time. Delay in one of the activities may affect the oth- er. In contrast, livestock activities are neither seasonal nor they have sequential effect upon each other. There- fore, the later activities are usually carried out by family labor. Livestock management in the study area was found as a full time job for one family member of a household in the study area. Forest fodder collection and grazing were the most time consuming activities for the live- stock management. Crop production consumed family as well as hired labor but livestock production mostly depended upon the family labor. Farmers reported that family labor was not enough during the peak period of crop cultivation. Therefore, hired labor was essential to perform several activities in time. Table 3 shows family labor calculation in three farm categories. It was calculated according to the labor-days available in the farming activities. The same method of family labor calculation was adopted by Regmi (1992). Labor-days (LD) available for farming activities per month was calculated based on the age and health con- dition of the each member. Finally, labor per month was converted into annual labor hour available for farming. C. Livestock and feed resources Livestock contributes significantly to the sustainability as well as household income of a farming family. There- fore, it has been considered as a major resource of the farm. The major ruminant animals reared by the farm- ers of study area were milking cow, buffalo, bullock and goats. They receive high income from milk and meat trading. Therefore, milking cow, buffalo, draft bullock and goats were considered as source of economic return in the farm model. The livestock used in the model were of local breads. Table 4 shows the number and types of livestock reared by the three farm categories. Livestock in the study area were mainly reared on crop residue, crop- by products, tree leaf fodder from farm land as well as supply from common property resources and wasteland through grazing, cut grasses/weeds and leaf fodder. Furthermore, they were fed with the home produced maize flour and by-products such as rice bran as con- centrate feed. Improved fodder grasses and forage crops plantation was not common in general. Table 5 shows feed supply from various sources, which were consid- ered as maximum feed supply in the farm model. Feed supply has been considered in term of Total Digestive Nutrient (TDN). Results and Discussion Optimization of Livestock Holding Using LP method The study attempted to formulate the optimum number and combination of livestock that should be reared by the households with different resource holdings. To for- mulate the optimum number and composition of live- stock in crop-livestock integrated farming system, the study used linear programming as a main analytical tool. Using the shadow prices of decision variables and the sensitivity analysis, different combination of livestock number, which gave maximum income to the farm household, were selected as optimum herd size. Since the livestock population of subwatershed was above the carrying capacity of resources, optimum herd size was formulated without significantly increasing their exist- ing herd size (Table 6). Optimum livestock holding for small farm size The representative of small farm size in the study area consisted of six members with an average of 2 members under age group 0-15 years and 3 members belonging to 16-59 years. The small farm size had annual family la- bor of 7852 hours (981 man- days). In an average a farm household in this category collected 3.8 mt/yr TDN from different sources. The total cultivated land holding size of small farm category was 0.43 ha out of which ir- rigated land is 0.17 ha and unirrigated land 0.26 ha. Rice was mainly grown in lowland (irrigated) areas whereas maize was grown in upland area (unirrigated). Besides crop production, the farmers under small farm category, reared in on average 1 milking cow, 1 milking buffalo, 1 bullock and 6 goats. With the existing resources, this farm category received 40133 NRs per year (Table  7). Table 4. Livestock holding by farm categories Types of Livestock Large Farm (n=47) Medium farm (n=57) Small Farm (n=58) Mean Std. Mean Std. Mean Std. Cow 1.5 1.47 1.4 1.4 1.2 0.84 Bullock 1.72 0.87 1.61 1.03 1.38 0.92 Cattle calves 0.33 0.79 0.21 0.64 0.28 0.61 Buffalo 1.72 1.16 1.19 0.98 1.43 0.77 Buffalo calves 0.82 0.76 0.52 0.61 0.48 0.89 Goat 5.88 3.10 5.08 4.00 5.55 2.18 Source: Household survey, Primary data 32 SQU Journal of Agricultural and Marine Sciences, 2017, Volume 22, Issue 1 Agricultural resources management trough linear programming The LP analysis revealed that the small farm categories with the above resources holding can optimize their herd size with 1 LU of buffalo and 4 LU of goat with 32% increase in gross income and 45% return in family labor Optimum livestock holding for medium farm size Medium farm family in the study area has total culti- vated land holding of 0.83 ha with irrigated and unirri- gated land 0.28 and 0.55 ha respectively. The household within the medium land holding consists of an average of 2 members belonging to age group 0-15 years and 3 members within age group, 15-59 years. The total annu- al family labor availability for farming activities is 7891 hrs (986 man-days). On an average, a farm household in this category collects 4.5 mt/yr of TDN from differ- ent source. The medium category of farm possess one LU of milking cow, one LU buffalo, 2 LU bullock and 1.5 LU goats (6 goats) and receives annual gross return of 49,158 NRs per year under the above mentioned crop and livestock activities whereas 2 LU of milking buffa- lo and 3.5 LU goats (14 goats) has been found as opti- mum livestock holding for medium farm family with the maximum use of above-mentioned land, labor and TDN supply. Medium farm family can increase their gross in- come with 35% and return at family labor by 49% with optimum herd size. Table 6. Optimum herd sizes for three categories of farm households. Decision variable Small Farm Medium farm Large Farm Gross Return (NRs) 53059.50 66711.84 91830.58 Cropping activities (ha) Rice 0.17 0.28 0.5 Maize 0.22 0.5 1 Fodder Plantation (ha) 0.04 0.08 0.2 Optimum herd size (LU) Cow - - - Buffalo 1 2 3 Bullock - - - Goat 4 (16 goats) 4 (16 goats) 4 (16 goats) Contribution of livestock (NRs*) 47516 (86%) 54956 (82%) 99884 (72%) Return over family labor (NRs) 170 173 195 * There is no indication Table 5. TDN supply from various sources of feed (kg/year). Types of Live- stock Large Farm (n=45) Medium farm (n=57) Small Farm (n=58) Mean Std. Mean Std. Mean Std. Rice Straw 480.25 410 329.02 273.45 245.69 296.56 Millet Straw 34.94 52 40.89 79.84 29.39 43.67 Wheat straw 4.26 11 4.77 17.0 4.18 12.5 Maize Stover 293 185 236.88 183.7 248.0 200.0 Maize cob 14.83 15.6 9.72 10.78 10.41 11.4 Pulse residue 3.56 0.88 3.8815 1.14 3.60 1.140 Maize flour 1036.11 1867 685.45 419.67 585.42 278.8 Rice bran 95.86 195 58.46 120.67 16.2 62.5 Farm grass 1711.90 361.6 310.24 321.4 285.30 457.7 Fodder tree 480.24 1138 310.24 178.6 285.30 222.6 Forest fodder 1175.82 494.7 1958.742 690. 1819.96 641.7 Grazing Supply 274.68 158.43 268.26 133.5 269.72 164.0 Total 5606 4506 3803 Source: Household survey, Primary data 33Research Article Jayasuriya and Das Optimum livestock holding for large farm size Large farm size in the study area possessed compara- tively higher resources than the other two farm catego- ries. It has total cultivable land holding of 1.75 ha with 1.2 ha irrigated (Khet land) and 0.55 ha of irrigated up- land (Bari land). Households in large farm size category consists of two members belonging to age group 0-15 years, three members between age 16-59 years and one elder member of more than 60 years of age. The total family labor availability in large farm size is 7929 hrs/yr (991man-days/yr). On an average, a farm household in this category collects 5.6 mt/yr of TDN from different sources. A farm household receives annual gross return of NRs 76745 per year with 0.5 and 1.2 ha of land al- Table 7. Comparison of system economics of current and simulated for all farm categories and three optional plans with re- spective gross returns to choose Farm Category Decision variables Existing farm plan Improved farm plans (LP simulated) Plan 1 Plan 2 Plan 3 Cropping activities (ha) Rice 0.17 0.17 0.17 0.17 Maize 0.26 0.22 0.22 0.22 Fodder - 0.04 0.04 0.04 Small Livestock activities (LU) Cow 1 1 - - Buffalo 1 1 1 1 Bullock 1 1 1 - Goat 1.5 (6 goats) 2 (8 goats) 2.8 (11 goats) 4 (16 goats) Gross return (NRs) 40 132 13 432 47341 53060 Contribution of livestock (Nrs) 74% (36 2012) 76% (37 658) 78% (42 898) 82% (54 956) Cropping activities (ha) Rice 0.28 0.23 0.23 0.23 Maize 0.55 0.5 0.5 0.5 Fodder - 0.08 0.08 0.08 Medium Livestock activities (LU) Cow 1 1 - - Buffalo 1 1 1 2 Bullock 2 2 2 - Goat 1 (4 goats) 1.3 (5 goats) 2 (8 goats) 4 (16 goats) Gross return (NRs) 49 158 50 526 54 653 66 712 Contribution of livestock (Nrs) 74% (36 212) 76% (37 658) 78% (42898) 82% (54956) Cropping activities (ha) Rice 0.5 0.5 0.5 0.5 Maize 1.2 1 1.0 1.0 Fodder - 0.2 0.2 0.2 Large Livestock activities (LU) Cow 1 1 - - Buffalo 2 2 2 3 Bullock 2 2 2 - Goat 1.5 (6 goats) 1.7 (7 goats) 2 (8 goats) 4 (16 goats) Gross return (NRs) 76 745 75 414 78 552 91 831 Contribution of livestock (Nrs) 67% (48 826) 66% (50 310) 68% (53 606) 72% (66 884) For goats 1LU=4 adult goats 34 SQU Journal of Agricultural and Marine Sciences, 2017, Volume 22, Issue 1 Agricultural resources management trough linear programming located for rice and maize respectively as well as from livestock activities. Livestock herd in this farm category is composed of a pair of buffaloes, a pair of bullocks, one cow and six goats. Since the large farm category has comparatively high- er resources holding than other farm categories, they are able to rear up to 3 LU of buffalo. Thus the large farm categories can optimize their livestock holding up to 3 LU of buffalo and 4 LU of goats (16 goats) with 19% increase in gross return and 40% increase in return at family labor. Other optional crop-livestock plans In addition to the constraints on economic and direct resources for crop-livestock activities, other sociological and agro-ecological aspects can be incorporated in the system by proper modelling and mathematical conver- sions of such linear functions. As an example, farmers in some systems can have a milking cow for family nutrient supply or a bullock for land preparation and transpor- tation by sacrificing a little reduction in optimum eco- nomic return. Table 7 shows the optimum crop-livestock combina- tions under three such plans compared with the current systems, in which farmers can chose the appropriate plan considering their conditions and requirements. Respective optimum economic returns under each plan and crop-livestock optimization was based on sensitivity analyses conducted in the program. Smaller farms show the highest livestock contribution contrarily by large farms. Three plans shows increasing trend of livestock contribution, the Plan III showing the optimal condi- tion. Some additional benefits due to increase in live- stock number were not taken in to the analysis such as soil nutrition improvement by the increased dong ma- nure generation etc. Conclusion Findings of the linear programming revealed that with the current feed resources capacity, farmers in the study area could maximize their farm income from crop-live- stock system without creating excessive pressure on the land resources and contribute towards sustainability of resources at the same time. Since the resources holding of farmers varies among each other, livestock carrying capacity at the household level also varies with farmers with different resources capacity. Farmers in the large, medium and small farm cate- gories can raise livestock up to 3 LU buffaloes and 4 LU goats, 2 LU buffaloes and 4 LU goats and 1 LU buffa- lo and 4.4 LU goats respectively according to their re- sources capacity. Farmers of these farm categories can maximize their benefit up to 19%, 34% and 32% from the improved farm plan with high return at the family labor than the existing farm plan. In all proposed farm plans I to III, contribution of livestock in gross return was found higher in small and medium farm categories than in the large. It indicates that a livestock enterprise in the study area is most profitable for low resource holding farm- ers. Among the herd composition, buffalo and goat rear- ing have proven more promising than cattle in terms of profit maximization. Furthermore, high return to the farm household la- bor shows potential for solving the problem of unem- ployment and under employment. Gross margin anal- ysis in all improved farm plans showed high return at family labor reflecting better employment opportunities of the farm labor in all farm categories. 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