Optimizing the Potential of Agricultural Land to Maintain the Production Sustainability (Empirical Study at West Papua)

West Papua is one of the provinces in Indonesia that has great land potential to be utilized as agricultural land, but this land has not been optimally utilized to support agricultural activities and yields in West Papua. This research aims at determine the land optimization model and determining the optimal agricultural land area in West Papua Province. This research uses a quantitative approach with secondary data and the data collection is conducted by documentation method. The analysis used in this research is Linear Programming. The results of research indicate that the optimal land area to be used as agricultural land in West Papua Province for food crops and horticulture is 1.60% and the land area for plantation crops is 2.31% of the existing land area without reducing the area forest area in West Papua Province.


Introduction
The economic condition of a country can be said to be good if the country is able to utilize the important and strategic economic sectors in accordance with its resources and geographical conditions [11].Indonesia has great potential in utilizing the important and strategic sectors such as agriculture because it has abundant natural resources, adequate land, and good climatic conditions for farming [13].
The agricultural sector plays an important role in human life in providing people's food needs for daily life survival [17; 18; 23], as a support for industrial raw materials [10], to increase people's income, to provide jobs [30; 32], as a source of foreign exchange earnings [1], and as a provider of environmental services to maintain environmental sustainability amidst climate change problems and global warming.Moreover, internationally, agriculture is still the main livelihood for 40% of the world's population and contributes to 30% of GDP in developing countries [26].This also occurs in Indonesia, based on the data published by the Central Bureau of Statistics (BPS) in August 2022, in which the sector that absorbs the most Indonesian workers is the agricultural sector.The diagram in Figure 1 shows that the agricultural sector becomes the one that absorbs the most workers in Indonesia in 2022 with a percentage of 29.76%.This percentage is up from the previous year which was 27.53%.While the trade sector is in the second place that contributes 19.23%, followed by the industrial sector in the third place in absorbing the Indonesian workers with a percentage of 13.61%, the food and beverage accommodation sector and the construction sector with respectively the percentage of 6.65% and 6 .28%.
It can be said that agricultural sector is the important determinant in meeting people's food needs and providing employment in Indonesia, so that in the future the development in agricultural sector will continuously be the important and strategic one in Indonesia and will have a balanced position with the development in other economic sectors.
West Papua is one of the provinces in Indonesia that has quite great potential for agricultural land with a percentage of land area of 5.21% of Indonesia's total area or 102,946.15square kilometers.Land resources of a region have an important role in developing the potential of its resources [27; 37] especially in agriculture, land resource plays an important role in supporting the agricultural production of an area.
Reported from [19] during a visit to West Papua, President Joko Widodo said that regions in Eastern Indonesia, especially West Papua, have quite extensive agricultural land and have great potential as the provider of food and horticultural commodity needs to support food ingredients in Eastern Indonesia.However, agricultural land in West Papua has only been utilized by 33% of the total agricultural land owned, so that the agricultural commodities produced also tend to be small.Based on the diagram in Figure 2, the greatest contributors of agriculture in Indonesia are dominated by provinces on the islands of Java and Sumatra, with the first place occupied by East Java Province with a GRDP value of Rp 167,304 billion in 2022.In the second place is North Sumatra Province with a GRDP value of Rp 136,332 billion rupiahs.In the third place is Riau Province with a GRDP value of Rp 135,315 billion rupiah, followed by Central Java Province and West Java Province, respectively with a GRDP value of Rp 126,256 and Rp 106,992 billion.Meanwhile, West Papua Province is one of the five lowest provinces that contribute the smallest to GRDP after DKI Jakarta, North Maluku and Riau Islands, with an area of 102,946.15km2 and a GRDP of Rp 6.122 billion in 2022.This is very unfortunate considering the area of land in West Papua with the potential for agricultural activities but has not been optimally utilized so that the agricultural contribution is not proportional to the area owned.

Method of Research
The type of research used is quantitative.The data used in this research is secondary data while the data sources are obtained from the official website publications of the Ministry of Environment, the Statistics of the Ministry of Agriculture, the Central Bureau of Statistics, and other related agencies.The analytical tool used in this research is Linear Programming.
According to [16], linear programming is a technique used to solve a problem or to make a decision in allocating limited resources so that it can be optimal, so that the results can be used for various purposes which are carried out using a quantitative analysis approach.[22] states that optimization indicates a finding of maximum and minimum values.Maximization is the process of obtaining the maximum value of an objective function with respect to optimal allocations such as maximum profit and minimum cost [12].Optimization can also be interpreted as an action to achieve something in the best condition from a decision problem under the limitations of available resources [29].
The final purpose of optimization itself is to maximize the benefits or to minimize the desired effort, so it can be concluded that optimization is related to the optimal allocation of limited available resources to maximize or minimize certain goals [2; 9; 33].
The optimization that will be conducted in this research is optimizing the agricultural sector to achieve the right solution in maximizing the agricultural potential in a region.The mathematical model The objective function is used to explain the purpose of research, to maximize or minimize something, in which this function is a linear equation of the objective variable.Meanwhile, the boundary function is an equation used to explain limitations or constraints that have a correlation with the resources faced in achieving the goal [25].
According to [16], the linear programming in general is as follows: Objective Function (FT) With Limitation (DP) where: Z is optimal value of objective function, Xj is types of activities (Decision Variable), aij is needs of resource i to produce each unit of activity j, bi is the number of available resource I, cj is increase in value Z if there is increase of one unit of activity j, a,b, and c is model parameter, m is the number of available resources, n is the number of activities.
The following are some of the requirements or criteria that must be met in formulating a linear programming model: • The objective function must be expressed in the form of a linear function, as the goal to be achieved.• The resources are available in limited quantities and the limitations must be expressed in the form of a linear inequality.• There must be alternative solutions that meet all constraints/limitations.

Result of Analysis
The optimization model consists of two functions, the objective function and the boundary function.The objective function in this research is to optimize the area of land use in order to maximize the GRDP productivity resulting from each type of the land use, in which the demand is divided into two, food crops and horticulture (X1) with existing land in the form of wet and dry agricultural land, plantations (X2) with existing land in the form of plantation land, according to the type of land use, assuming that the parameter is the GRDP productivity received from each land use per hectare (million rupiahs/hectare).Based on these assumptions, the objective function equation in this research is: The boundary function of the objective function consists of several factors that can become obstacles in optimizing the allocation of agricultural land.The surrounding land use factor is not directly included in the boundary function, but there will still be a reduction in the total land area because the land is used for other activities, such as forest areas, transmigration, mining, airports/ports so that the land area that can be optimized is 10,644.890 Ha is 881,382.18Ha.
The first boundary function is social demography.It is a limitation because the population will continue to increase every year so that the need for residential land will also increase [20].In the Spatial Plan (RTRW) of West Papua Province in 2013-2033 the land allocated as a residential area is 456,950 5 Ha.So that from the land area of 881,382.18Ha there are 415,432.18Ha that can be optimized as agricultural cultivation areas, with the boundary function which can be written as follows: The second boundary function is existing land, in which the area of land to be optimized must maintain the existing land area for food crops and horticulture with an existing land area of 114,876.12Ha and plantations of 113,681.36Ha.So that the cultivation area that can be optimized is no less than the existing agricultural land that is owned so that the function of the existing land boundaries is: The last boundary function used in this research is institutional boundary function.This institution refers to Regional Regulation number 4 of 2013 RTRW 2013-2033 of West Papua Province.For wet land agriculture the minimum area is 26,579 Ha, while for dry land agriculture it is 17,552 Ha, and for plantation agriculture the maximum area is 245,536 Ha.So that the function of the institutional boundaries of West Papua Province is as follows: Optimization analysis in this research uses the Lingo 18 software tool, which is conducted by inputting all formulations, both the objective function and the boundary function that have been compiled into the software for processing.After conducting the input, an output will be obtained in the form of a solution to determine the optimal allocation of agricultural land area in West Papua.Based on table 1 above, it can be seen that each optimal land area is as follows: the land area for food crops and horticulture (X1) is 169,859.2Ha, and the land area for plantation crops (X2) is 245,536.0Ha from the land area that can be optimized amounted 415,432.18Ha.These results indicate that the reduced cost value of each variable is 0, which means that all the boundary functions in this research have been fulfilled in the model or it can be said that there is no change in the optimal value of the objective function for each variable, so this modeling is feasible to use.It is in accordance with the results of research [5], which states that reduced costs are always zero for optimal solutions.These results are also consistent with a research [15] stating that if the reduced cost value for each variable is zero then all variables have reached the optimal conditions.
After the solution results of the optimal land use have been obtained, the validity of the output that has been produced should be tested by conducting a sensitivity test.This test was conducted with the aim of knowing the magnitude of the influence of changes in each variable on the boundary function and the objective function in a tolerable model, so that no changes occur in the optimal value that has been produced.The following are the results of the sensitivity test as shown in the range report table as follows: Table 2 Based on table 2 above, it can be seen that the results of the sensitivity test show that the equation values for the results are in accordance with the established equation limits, so it can be concluded that the allowed change values are in accordance with the limits of all predetermined formulas, for technical limits that the value of X1 and X2 ≥ 0 have also been fulfilled, so this model is feasible to use.These results are in accordance with research [14] stating that the model is appropriate to use if it is in accordance with the lower limit and upper limit of the formula that has been determined.
The availability of land plays an important role in supporting agricultural activities in an area.This is because the agricultural production depends on the optimal land use for crop cultivation [35; 40; 39].Land resources are a step to determine the balance between availability and demand for land use and utilization based on the use of a particular area [31].[28] also state that increasing the efficiency of agricultural production is determined by the structure of land use.
The optimal use of agricultural land is expected to increase the agricultural production to be effective and efficient to meet food demand or needs [3; 22], especially in West Papua Province.[4] also state that the proper distribution of land allocation will affect the level of agricultural production and efficiency in general, such as increasing employment so that it will have an impact on higher community incomes.Efforts that can be made are by re-managing agricultural land that has been abandoned or opening new agricultural land (extensification) [39].However, in opening the new land, some further land management efforts are still needed to support the agricultural activities such as managing soil fertility, analyzing land suitability and suitable plant species, determining cropping patterns taking into account climatic conditions, managing irrigation or constructing canals.

Conclusion
The results of this research indicate that from the formulation that has been conducted, the optimal model for optimizing the use of agricultural land in West Papua Province is feasible to use with the objective function Max D = 4.9X1 + 5.2X2.Meanwhile, the boundary function is X1 + X2 ≤ 415,432.18;X1 ≥ 114,876.12;X2 ≥ 113,681.36;X1 ≥ 44.131 and X2 ≤ 245.536.For agricultural land area, the optimal allocation of land to be used as agricultural land in West Papua Province for food crops and horticulture (X1) is 169,859.2Ha (1.60%) and the land area for plantation crops (X2) is 245,536.0 Ha (2.31%) of the existing land area.From the results of this research, it is expected that the local governments and the local communities can work together to utilize the land uses that are potential to become agricultural areas to increase agricultural production in meeting the demand or food needs in Eastern Indonesia.

2 Figure 1 .
Figure 1.Employment Percentage based on Sectors in 2022 Source: Central Bureau of Statistics, 2022

Figure 2 .
Figure 2. GDRP of Agricultural Sector based on Constant Price (Billion Rupiahs) based on Provinces in Indonesia in 2022 Source: Central Bureau of Statistics, 2022 linear programming to describe the problem to be analyzed.The form of the model consists of two forms of function, the objective function and the boundary/constraint function.
4is used in

Table 1 .
Solution Report . Range Report of Sensitivity Test