Optimization of land use for food crops a case in Gunung Sari District West Lombok Regency, Indonesia

This study aims to identify farmer’s crops in each growing season, analyze the income of food crops farmers, analyze the optimal use of land resources, know the problem of farmer food crops in Gunung Sari District West Lombok Regency. Method of this research is descriptive and data collected by survey techniques. The results showed MT1 were rice crops, MT2 included rice, peanuts, sweet corn, soybeans, and MT3 included peanuts, soybeans, sweet corn, green beans, rice, long beans. Farmer’s income of rice farming on MT1 is IDR 13,081,495.95/ha. The largest Farmer’s income on MT2 is the sweet corn farming of IDR 13,993,518.52/ha and the smallest income in rice farming is IDR 11,625,009.81/ha. The largest farmer’s income on MT3 is long bean farming IDR 22.039.404,76/ha, and the smallest is the big peanut IDR 8,919,248.24/ha. Optimal utilization of land resources in MT2 that is X2 (nuts) of 159,020 ha, X3 (sweet corn) of 256,417 ha and X4 (soybean) of 325,142 ha. MT3 optimal land use area X2 (soybean) of 434,659 ha, X3 (sweet corn) 126,969 ha and X6 (long bean) of 178,953 ha. Problems of farmers include pests, diseases, lack production facilities, the high input price and the unavailability of cooperatives.


Introduction
Land use that is not in accordance with its potential will result in decreased productivity, degradation of land quality and is not sustainable.In order to avoid this, it is necessary to evaluate the land to support sustainable agricultural development planning [1,2].Utilization of land resources needs to be adjusted to the agroecological conditions, so that agricultural businesses can be sustainable.To be able to support a utilization of land resources requires knowledge about the nature of the land and how to combine the selection of business activities.For this reason, a parametric Linear Programming approach can be used which includes a system of classification and division of land based on the effects or values of certain land characteristics and then combining these influences to obtain the appropriateness [3].
Potential of food crops that can be developed in Gunungsari, West Lombok Regency include: rice, corn, cassava, sweet potatoes, peanuts, soybeans and green beans [4].Paddy productivity is 53.20 kw/ha with a harvested area of 1,827 ha.The productivity of cassava is 162.73 kw/ha with a harvested area of 109 ha, while the productivity of sweet potato is 179.27 kw/ha with a harvested area of 3 ha.In addition, the productivity of peanuts is 9.57 kw/ha with a harvested area of 101 ha and soybeans is 12.70 kw/ha with a harvested area of 420 ha.For the green bean commodity, productivity is 18.19 kw/ha with a harvest area of 3 ha [5,6].
Judging from the availability of agricultural resources which tend to be increasingly limited, agricultural land which tends to decrease due to land conversion, limited capital, and input prices which

Types of food crops cultivated in each planting season
There are types of food crops that are cultivated in (Season-1, Season-2, Season-3) for a year.Season-1 includes: rice.Season-2 includes: rice, peanuts, sweet corn and soybeans.Season-3 includes: peanuts, soybeans, sweet corn, green beans, rice and long beans.

Revenue analysis
Farming Income Analysis Season-1.Total production costs, production, production value (receipt), and income in Season-1 rice farming in Gunungsari are presented in Table 1.  1 shows that the average total production costs incurred by farmers in Season-1 rice farming is IDR 6,952,748/ha.Labor costs 75%, input costs 21%, and fixed costs 4%.The average production of Season-1 rice farmers in Gunungsari is 5,614 kg/ha, with an average harvest dry grain (GKP) price of Rp. 3,555/kg, so that an income of Rp. 20,034,244/ha is obtained.Furthermore, farming income is the difference between production value and total production costs, so that farmers' income from rice farming is IDR 13,081,495.95/ha.The R/ C value of Season-1 rice farming was 2.88 (R/C > 1) indicating that rice farming in Gunungsari was financially feasible because it could provide a profit of 1.88 (2.88-1).Farming Income Analysis Season-2.The total cost of production, production, income and income on Season-2 farming in the Gunungsari is presented in Table 2. Table 2 shows that of the four types of Season-2 farming activities, the largest average total production cost incurred by farmers is sweet corn farming, which is IDR 11,006,481.48/ha.The high cost of production in corn farming is due to the large cost of production facilities, which is IDR 5,550,000/ha.The high cost of production facilities is mainly due to the high cost of purchasing sweet corn seeds (Rp 4,000,000/ha).The average price of sweet corn seeds is Rp.300,000/kg, so with an average use of sweet corn seeds by farmers of 133 kg/ha (rounded number), the purchase cost of seeds is Rp.4,000,000/ha.Apart from sweet corn, the production cost which is quite large is peanuts, which is IDR 7,583,738.05/ha;followed by soybeans and rice.In terms of income, the biggest income was obtained from sweet corn farming, which was IDR 13,993,518.52/ha,followed by peanut, soybean and rice farming.Meanwhile, sweet corn farming has an R/C value of 2.27 (R/C>1) which means that sweet corn farming in Gunungsari is financially feasible because it can provide a profit of 1.27 (2.27-1) .
Farming Income Analysis Season-3.The total costs of production, production, revenue and income on Season-3 farming in the Gunungsari are presented in Table 3.The results of the analysis using linear programming with primal solutions can be obtained information that out of the 4 types of food crop farming activities, there are 3 activities included in the basis.This indicates that the three food crop farming activities (peanuts, sweet corn and soybeans) are the recommended types of food crops, because they can maximize the income of farmers in the Gunungsari area of IDR 9,320,563,010.-.Table 4 shows that the activity of food crops selected for the optimal solution of solving the primal problem (base) is farming activity X2 (Peanut), X3 (Sweet Corn), and X4 (Soybean).This is marked by the inclusion of these activities into the basis and has a net cost value of zero.This means that the business scale of the three activities has provided maximum income, and it is not profitable if the business scale is added.In the primal solution, it can also be seen that the activity that was not selected as the optimal solution (non-base), namely farming activity X1 (rice) has a negative net cost value (-990,500), indicating that operating activity (X1) is not profitable, because the addition one unit of activity causes a decrease in the value of the optimal program by the value of the net cost.The size of the suggested farming activity scale is shown by the value.For example, the value of the peanut farming activity (X2 ) is 159.020,meaning that the peanut farming activity (X2 ) is suggested to be developed in an area of 159.020 ha.In addition to activity X2, the recommended activities are activity X3 (sweet corn) covering an area of 256.417 ha; and activity X4 (soybean) covering an area of 325.142 ha.On the other hand, farming activities that have a value = 0, namely rice farming activities (X1) provide information that these activities are not selected in the optimal solution and are advised not to be cultivated.
Dual Completion of Season-2 Farming Activities.The results of the analysis of optimizing the use of land resources and other resources in various Season-2 food crop farming activities (primal settlement), it appears that, there are agricultural resources or agricultural inputs (CFi) that have a binding Category (B) with a positive dual value and non-binding Category with a dual zero value, presented in Table 5.The results of solving the dual problem (Table 5), show that resources that have a positive "dual value" (binding) > 0 are CF 1 (land area) of 7,903.22;CF 6 (fertilizer Urea) of 3.356; and CF 13 (labor in the family) of 217,485.The dual value of CF 1 (land area) is 7,903.221,meaning that each additional land area resource in Season-2 of one unit (other resources remains constant) will increase the optimal solution (income) by IDR 7,903,221.Likewise for CF 6 resources (fertilizer Urea) of 3.356 means that the addition of CF6 resources (fertilizer Urea) of one unit (other resources are fixed) will increase the optimal solution (income) by Rp. 3,356, -; and the value of " dual value " for CF 13 (labor in the family) of 217,485 means that the addition of CF 13 resources (labor in the family) of one unit (other resources are fixed) will increase the optimal solution (income) Rp. 217,485, -Sensitivity Analysis of Season-2 Farming Activity Optimization Results.The results of the sensitivity analysis on effort.i Season-2 food crops in Gunungsari are demonstrated through the completion of objective row ranges.Based on the results of the sensitivity analysis, there is a sensitivity range with a certain "minimum limit" and "maximum limit" for the possibility of a change in income for each activity (X 1 , X 2 , X 3 , and X 4 ), presented in Table 6.The sensitivity range values that are included in the basis for activity X2 (peanuts) are: a minimum (lower limit) of 10,615.347and a maximum (upper limit) of 12,907.645.This range value means that changes to the optimal program value (value) will not occur if the income per hectare obtained by activity X 2 (peanuts Rp. 12,203,883/ha) decreases to Rp. 10,615,347 (lower limit) or increases up to IDR 12,907,645,-/ha (upper limit).So if there is a change in the average peanut production (increase/decrease) or a change in the output price (increase/decrease) in peanut products which ultimately changes the average peanut farming income, then as long as the change in the average peanut farming income the land referred to is still within the lower limit and upper limit range, the stability of the optimal program value will not change (stable).Likewise for other Season-2 farming activities that are included in the Season-2 base, namely X 3 (sweet corn) and X 4 (soybeans).
From the results of the sensitivity analysis on the optimal program value to changes in agricultural resources (inputs) in various Season-2 food crop farming activities in the completion of right hand side ranges, it can be seen the degree of sensitivity of agricultural resources (inputs) to the optimal program value of farming activities Season-2.
Resources that have binding Category, namely CF 1 (land area), CF 6 (fertilizer urea), and CF 13 (Labor in the family) is a resource that is used up in optimal planning of food crop farming activities that earn an income of IDR 9,320,563,010, can be presented in Table 7.The dual value for CF 1 resources (land area) is 7,903.221(Rp.000), indicating that the addition of land area resources in Season-2 farming by one unit (ha) will increase income by Rp. 7,903,221, -/ha,-.The estimated value of this optimal program will be stable if changes in land area availability in Season-2 are still within the range of the minimum sensitivity limit of 725.279 ha and a maximum of 753.507 ha; resource CF 6 (Urea fertilizer) is 3.356 indicating that the addition of Urea fertilizer resources in Season-2 farming by one unit (kg) will increase income by IDR 3,356, -/ha.still within the range of the minimum sensitivity limit of 27,706.314kg and a maximum of 161,697.263kg.CF 13 resources (labor in the family) is 217,485, indicating that the addition of family labor resources in farming by one unit (HKO) will increase income by Rp. 217,485, -/ha, -.The estimated optimal program value will be stable if changes in the availability of labor in the family in Season-2 are still within the range of the minimum sensitivity limit of 13,605.69HKO and a maximum of 14,135.787HKO .So, if there is a decrease in resource availability in Season-2 food crop farming, then the estimated optimal program value will remain stable if the decrease in resource availability is not lower than the minimum limit and if there is an increase in availability, then the estimated optimal program value will not change during the addition.does not exceed the maximum tolerance limit.
Based on the analysis of solving primal and dual problems, the use of land resources is optimal for various food crop farming activities at Season-2 in Gunungsari .The amount of optimal use for other agricultural resources which includes seed/seedling production facilities, fertilizers, labor within the family and outside the family according to the recommended land area for the three activities (activity X 2 , X 3 , and X 4 ).The values in "brackets" indicate the value per hectare , presented in Table 8. a (…) shows the use of production facilities and labor per hectare.
Table 8 shows the amount of optimal use for other agricultural resources which includes seed/seedling production facilities, fertilizers, labor within the family and outside the family according to the recommended land area for the three activities (activity X2 , X3 , and X4 ).The values in brackets indicate the value per hectare.Analysis of optimizing the use of land resources for Season-3 food crop activities on primal analysis.Analysis of the calculations using linear programming with primal solutions can be obtained information that of the 6 types of food crop farming activities, there are 3 activities included in the base.This shows that the three farming activities (soybeans, sweet corn and long beans) are recommended types of food crops, because they can maximize the income of farmers in the Gunungsari area, which is Rp.13,730,871.822,-. presented in Table 9.
Table 9 shows that the activity of the food crops selected for the optimal solution of solving the primal problem is farming activity X 2 (soybean), X 3 (sweet corn) and X 6 (long bean).This is indicated by the inclusion of these activities into the base and having a net cost value of zero, meaning that the scale of the three activities has provided maximum income, and it is not profitable to add to the scale of enterprise.In the primal solution it can be seen that the activity that was not selected as the optimal solution (nonbase), namely farming activity X1 (peanuts) has a negative net cost value (-7637.112),indicating that the exploitation of the activity (X1) is unprofitable, because the addition of one unit of activity causes a decrease in the value of the optimal program (income) by the value of the net cost .The size of the recommended Season-3 farming activity scale is shown by the value.For example, the value of soybean farming activities (X2) is 434,659, meaning that soybean farming activities (X 2 ) are suggested to be developed for an area of 434,659 ha; activity X 3 (sweet corn) covering an area of 126,969 ha; and activity X 6 (long bean) covering an area of 178,953 ha.Farming activities that have a value = 0, namely peanut farming activities (X1), green bean farming (X4), and rice farming (X5).This shows that the three farming activities are not selected in the optimal solution and are advised not to be cultivated.

Dual Completion of Season-3 Farming Activities.
Results of the analysis of optimizing the use of land resources and other resources in various Season-3 food crop farming activities, there are agricultural resources or agricultural inputs (CFi) that have a binding Category (B) with a positive dual value and a non-binding Category with a dual value zero.The results of the optimization analysis on solving dual problems are presented in Table 10.
From the results of solving the dual problem (Table 10), resources that have a positive "dual value" (binding) > 0 are CF 1 (land area) of 14,739.013;CF 8 (fertilizer Urea) of 4,356; and CF 15 (labor in the family) of 144,230.The dual value of CF 1 (land area) is 14,739.013,meaning that each additional land area resource of one unit (other resources remains constant) will increase the optimal solution (income) Rp. 14,739.013,-/ha; for CF 8 resource (fertilizer Urea) of 4.356 means that the addition of CF 8 resources (fertilizer Urea) of one unit will increase the optimal solution (income) by IDR 4,356; and for CF 15 (labor in the family) of 144,320, it means that the addition of CF 15 (resources) by one unit will increase the optimal solution (income) Rp. 144,320, -.Sensitivity Analysis of Season-3 Farming Activity Optimization Results.The results of the sensitivity analysis on Season-3 food crop farming are shown by completing the objective row ranges.The results of the sensitivity analysis, there is a sensitivity range with a certain "minimum limit" and "maximum limit" for the possibility of a change in income for each activity (X1, X2, X3, X4, X5, and X6) is presented in Table 11.The range of activity sensitivity values included in the basis, namely: activity X2 (soybean) has a minimum (lower limit) of 16,054.297and a maximum (upper limit) of 18,012.217.The range value means the change in the optimal program value (value) will not occur if the income per hectare obtained by activity X2 (soybean Rp 17,031.116/ha)decreased to IDR 16,054,297 or increased to IDR 18,012,217/ha.So if there is a change in the average soybean production (increase/decrease) or a change in the output price (increase/decrease) of soybean products which ultimately changes the average income of soybean farming, then as long as the change in the average income of soybean farming is still in the lower limit and upper limit range, the stability of the optimal program value will not change (stable).
Likewise for other farming activities that are included in the basis, namely X 3 (sweet corn) and X 6 (long beans).
(Urea fertilizer) is 4.356 indicating that the addition of Urea fertilizer resources in Season-2 farming by one unit (kg) will increase income by IDR 4,356/ha.The estimated optimal program value will stabilize when changes in Urea fertilizer availability still within the range of the minimum sensitivity limit of 98,614.051kg and a maximum of 170,210.716kg and CF15 resources (labor in the family) is 144,230, indicating that the addition of family labor resources in farming by one unit (HKO) will increase income Rp.144,230/ha, -.The estimated optimal program value will be stable if changes in the availability of labor in the family are still within the range of the minimum sensitivity limit of 16,271,780 HKO and a maximum of 13,176,778 HKO.So, if there is a decrease in the availability of resources in food crop farming, the estimated optimal program value will remain stable if the decrease in resource availability is not lower than the minimum limit and if there is an increase in availability, then the estimated optimal program value will not change as long as the addition does not exceed maximum tolerance limit.
Optimum Use of Agricultural Resources for Various Food Crop Farming Activities Season-3.Based on the analysis of solving primal problems and solving dual problems, the optimal use of land resources for various food crop farming activities in Season-3 is presented in Table 13.

Conclusion
Based on the results of the research and discussion, the following conclusions can be drawn: (1) Types of food crops cultivated by farmers in the Gunungsari area in a year, for Season-1 include rice; Season-2 covers: rice, peanuts, sweet corn, and soybeans and Season-3 covers: peanuts, soybeans, sweet corn, green beans, rice and long beans; (2) The average total production costs Season-1 rice farming is IDR 6,952,748.32/ha.The average production is 5,614.04/ha;Rice farm income IDR 13,081,495.95/ha.Income (Season-2) from farming rice, peanuts, sweet corn, and soybeans, it is known that the biggest income is sweet corn, which is IDR 13,993,518.52, and the smallest income is paddy of IDR 11,625,009.81/ha;Income (Season-3) from farming peanuts, soybeans, sweet corn, green beans, rice and long beans, the largest income is long bean farming of IDR 22,039,404.76/ha; and the smallest income was peanuts of IDR 8,919,248.24/ha.; (3) Food crops in the Gunungsari area have a land area of 740.58 ha, for optimal use of land resources in (Season-2) which generates a total income of IDR 9,320,563,010, -with recommendations for optimal land use area, namely for activities X 2 (159,020 ha of peanuts), X 3 (256,417 ha of sweet corn); and X 4 (soybean area of 325.142 ha).Furthermore (Season-3) can generate a total income of IDR 13,730,871,822, -with recommendations for optimal land use area, namely for X 2 (soybeans covering an area of 434,659 ha), X 3 (sweet corn covering an area of 126,969 ha); and X 6 (long bean area of 178,953 ha).

Recommendations
(1) In order to obtain maximum income for food crop land, it is recommended to regulate the use of food crop land as follows: (a) Planting season (Season-2) it is recommended to cultivate three types of food crops, namely activity X 2 (peanut 159,020 ha), X3 (sweet corn 256.417 ha), and X4 (soybean 325.142 ha); (b) Planting season (Season-3) it is advisable to cultivate three types of food crops, namely activity X 2 (soybean 434,659 ha), X 3 (sweet corn 126,969 ha), and X 6 (long bean 178,953 ha); (2) It is suggested to farmers, especially in the Gunungsari area, to strengthen existing farmer groups so that they can better deal with the problems faced by farmers, both in overcoming problems in procuring production facilities, dealing with pests and diseases, and in marketing the produce; and (3) it is hoped that the government through related institutions will provide guidance to farmers, especially in the formation and or empowerment of cooperatives, especially in the research location area so that they can overcome the problems faced by farmers in the provision of production facilities in a timely manner, in the right quantity and right quality.

a X 1 =
Peanut farming activity Season-3 X 4 = Green bean farming activity Season-3 b X 2 = Soybean farming activity Season-3 X 5 = Rice farming activity Season-3 c X 3 = Sweet corn farming activity Season-3 X 6 = Long bean farming activity Season-3

Table 1 .
Average Total Costs of Production, Production, Revenue, and Income in Season-1 Rice Farming in Gunungsari West Lombok Regency, 2020

Table 2 .
Average total cost of production, production, revenue and income per hectare for season-2 farming in Gunungsari West Lombok Regency, 2020.

Table 3 .
Average Total Cost of Production, Production, Revenue and Income per Hectare for

Table 3
shows that of the six types of farming activities, the highest average production cost is sweet corn farming, which is IDR 11,296,691.01/ha,followed by long beans, green beans, soybeans, rice and peanuts.As previously explained, the high cost of production in sweet corn farming is due to the high price of seeds.

Table 5 .
Results of Problem Solving Analysis of Dual Season-2 Food Crop Farming Activities a CF = limiting factor (constraint factor); NB= nonbinding

Table 6 .
Values of the Sensitivity Range of Objective Function Coefficients (Objective Row Ranges) in Various Season-2 Food Crop Farming Activities in Gunungsari, West Lombok

Table 7 .
Value of agricultural resource sensitivity range in season-2 Food Crop Farming Activities in Right Hand Side Ranges a B = Bindings; b NB = NB ; c CF = Constraint factor

Table 8 .
Optimal Use of Resources for Various Season-2 Food Crop Farming Activities in Gunungsari, West Lombok Regency, 2020

Table 9 .
Results of Primal Problem Solving Analysis of Season-3 Food Crop Farming Activities in Gunungsari, West Lombok Regency, 2020Final optimal solution: Z = IDR 13,730,871,822

Table 10 .
Results of problem solving analysis of dual activities of food crop farming Season-3

Table 11 .
Values of the Sensitivity Range of Objective Function Coefficients (Objective Row Ranges) in Various Season-3 Food Crop Farming Activities in Gunungsari, West Lombok

Table 13 .
Optimal Use of Land Resources for Various Season-3 Food Crop Farming Activities Selected in Optimal Solutions in Gunungsari, West Lombok Regency, 2020