PRODUCT MODELLING TO SUPPORT PRODUCT DEVELOPMENT IN A VIRTUAL ENTERPRISE

The concept of Virtual Enterprise (VE) is closely related to the Global Manufacturing (GM) paradigm. A VE is established each time a new product development is required. How to develop a computer system which supports the product development in VE is an issue ti be discussed in this paper. The emphasis is placed on the product modelling in the VE context, and a new concept of information modelling called “heterogeneous data”situation is clarified, which is further related to the “Instance As Type”(IAT) phenomenon. Modelling for IAT is discussed.Modelling for the partner company behaviour is presented as well.

A Well Productivity Model for Multi-Layered Marine and Continental Transitional Reservoirs with Complex Fracture Networks

Using the typical characteristics of multi-layered marine and continental transitional gas reservoirs as a basis,a model is developed to predict the related well production rate.This model relies on the fractal theory of tortuous capillary bundles and can take into account multiple gas flow mechanisms at the micrometer and nanometer scales,as well as the flow characteristics in different types of thin layers(tight sandstone gas,shale gas,and coalbed gas).Moreover,a source-sink function concept and a pressure drop superposition principle are utilized to introduce a coupled flow model in the reservoir.A semi-analytical solution for the production rate is obtained using a matrix iteration method.A specific well is selected for fitting dynamic production data,and the calculation results show that the tight sandstone has the highest gas production per unit thickness compared with the other types of reservoirs.Moreover,desorption and diffusion of coalbed gas and shale gas can significantly contribute to gas production,and the daily production of these two gases decreases rapidly with decreasing reservoir pressure.Interestingly,the gas production from fractures exhibits an approximately U-shaped distribution,indicating the need to optimize the spacing between clusters during hydraulic fracturing to reduce the area of overlapping fracture control.The coal matrix water saturation significantly affects the coalbed gas production,with higher water saturation leading to lower production.

Productivity Prediction Model of Perforated Horizontal Well Based on Permeability Calculation in Near-Well High Permeability Reservoir Area

To improve the productivity of oil wells,perforation technology is usually used to improve the productivity of horizontal wells in oilfield exploitation.After the perforation operation,the perforation channel around the wellbore will form a near-well high-permeability reservoir area with the penetration depth as the radius,that is,the formation has different permeability characteristics with the perforation depth as the dividing line.Generally,the permeability is measured by the permeability tester,but this approach has a high workload and limited application.In this paper,according to the reservoir characteristics of perforated horizontal wells,the reservoir is divided into two areas:the original reservoir area and the near-well high permeability reservoir area.Based on the theory of seepage mechanics and the formula of open hole productivity,the permeability calculation formula of near-well high permeability reservoir area with perforation parameters is deduced.According to the principle of seepage continuity,the seepage is regarded as the synthesis of two directions:the horizontal plane elliptic seepage field and the vertical plane radial seepage field,and the oil well productivity prediction model of the perforated horizontal well is established by partition.The model comparison demonstrates that the model is reasonable and feasible.To calculate and analyze the effect of oil well production and the law of influencing factors,actual production data of the oilfield are substituted into the oil well productivity formula.It can effectively guide the technical process design and effect prediction of perforated horizontal wells.

Statecharts for Distributed Product Data Management System Modelling

Product data management (PDM) has been accepted as an important tool for the manufacturing industries. In recent years, more and mor e researches have been conducted in the development of PDM. Their research area s include system design, integration of object-oriented technology, data distri bution, collaborative and distributed manufacturing working environment, secur ity, and web-based integration. However, there are limitations on their rese arches. In particular, they cannot cater for PDM in distributed manufacturing e nvironment. This is especially true in South China, where many Hong Kong (HK) ma nufacturers have moved their production plants to different locations in Pearl R iver Delta for cost reduction. However, they retain their main offices in HK. Development of PDM system is inherently complex. Product related data cover prod uct name, product part number (product identification), drawings, material speci fications, dimension requirement, quality specification, test result, log size, production schedules, product data version and date of release, special tooling (e.g. jig and fixture), mould design, project engineering in charge, cost spread sheets, while process data includes engineering release, engineering change info rmation management, and other workflow related to the process information. Accor ding to Cornelissen et al., the contemporary PDM system should contains manageme nt functions in structure, retrieval, release, change, and workflow. In system design, development and implementation, a formal specification is nece ssary. However, there is no formal representation model for PDM system. Theref ore a graphical representation model is constructed to express the various scena rios of interactions between users and the PDM system. Statechart is then used to model the operations of PDM system, Fig.1. Statechart model bridges the curr ent gap between requirements, scenarios, and the initial design specifications o f PDM system. After properly analyzing the PDM system, a new distributed PDM (DPDM) system is proposed. Both graphical representation and statechart models are constructed f or the new DPDM system, Fig.2. New product data of DPDM and new system function s are then investigated to support product information flow in the new distribut ed environment. It is found that statecharts allow formal representations to capture the informa tion and control flows of both PDM and DPDM. In particular, statechart offers a dditional expressive power, when compared to conventional state transition diagr am, in terms of hierarchy, concurrency, history, and timing for DPDM behavioral modeling.

A new method to evaluate integrated production system capacity in oil fields

To improve the design and management of an integrated production system(IPS),a set of mathematical models and workflows are developed for evaluating the capacity of an IPS at steady-state conditions.Combining the conservation laws with applicable multiphase fluid and choke models,these mathematical models are solved to characterize the hydraulics of an integrated system of reservoir,wells,chokes,flowlines,and separator at steady state.The controllable variables such as well count,choke size and separator pressure are adjusted to optimize the performance of the IPs at a specific time.It is found that increasing the well count can increase the bulk flow rate of the production network,but too many wells may increase the manifold pressure,leading to decline of single-well production.Increasing the choke size can improve the capacity of the IPs.The production of the IPs is negatively correlated with the separator pressure.With increasing separator pressure and decreasing choke size,the increment of total fluid production(the capacity of IPS)induced by increasing well count decreases.Validation tests with field examples show a maximum absolute deviation is 1.5%,demonstrating the robustness and validity of the proposed mathematical models and workflows.

Revolutionizing Tight Reservoir Production: A Novel Dual-Medium Unsteady Seepage Model for Optimizing Volumetrically Fractured Horizontal Wells

This study presents an avant-garde approach for predicting and optimizing production in tight reservoirs,employing a dual-medium unsteady seepage model specifically fashioned for volumetrically fractured horizontal wells.Traditional models often fail to fully capture the complex dynamics associated with these unconventional reservoirs.In a significant departure from these models,our approach incorporates an initiation pressure gradient and a discrete fracture seepage network,providing a more realistic representation of the seepage process.The model also integrates an enhanced fluid-solid interaction,which allows for a more comprehensive understanding of the fluid-structure interactions in the reservoir.This is achieved through the incorporation of improved permeability and stress coupling,leading to more precise predictions of reservoir behavior.The numerical solutions derived from the model are obtained through the sophisticated finite element method,ensuring high accuracy and computational efficiency.To ensure the model’s reliability and accuracy,the outcomes were tested against a real-world case,with results demonstrating strong alignment.A key revelation from the study is the significant difference between uncoupled and fully coupled volumetrically fractured horizontal wells,challenging conventional wisdom in the field.Additionally,the study delves into the effects of stress,fracture length,and fracture number on reservoir production,contributing valuable insights for the design and optimization of tight reservoirs.The findings from this study have the potential to revolutionize the field of tight reservoir prediction and management,offering significant advancements in petroleum engineering.The proposed approach brings forth a more nuanced understanding of tight reservoir systems and opens up new avenues for optimizing reservoir management and production.

Advances and outlook of integrated reservoir-wellbore-pipe network simulation technology

The integrated simulation and optimization technology of reservoir-wellbore-pipe network is developed to reflect the mutual influence and restriction among reservoir engineering,oil production engineering and surface engineering,and to obtain the scheme with minimum conflict and optimal benefit in each step.This technology is based on the concept of global optimization to maximize production and profit,reduce costs and increase benefit.This paper elaborates the current situation of integrated simulation technology of reservoir-wellbore-pipe network both at home and abroad,discusses its correlation with the primary business of Sinopec and its development from three aspects of modeling,cloud platform and intellectualization.Suggestions on its future development are put forward from underlying data,software platform,popularization and application,and cross-border integration to provide means and guidance for the construction of intelligent oil and gas fields.The results show that the integrated simulation of reservoir-wellbore-pipe network can better reflect the optimization requirements of each step,avoid the ineffective operation of field equipment,and effectively improve the efficiency of research and management.Coupling solution,global optimization method and pressure fitting,which can make the simulation results reflect the real situation,are the key technologies for the network.The theoretical technology and main function research of integrated simulation technology have been mature,but the large-scale application and local function improvement of oil and gas fields are yet to be promoted.In the future,the integrated simulation of reservoir-wellbore-pipe network will develop from digitalization to modeling and intellectualization,from local simulation to cloud computing,and from manual intervention to intelligent decision-making.We suggest speeding up the construction of the unified database and model base of the whole underlying platform,strengthening the construction of software integration and integration platform with independent intellectual property rights,speeding up the popularization and application of intelligent oil and gas field demonstration projects,and strengthening the integration of oil and gas industry with artificial intelligence(AI),big data and block chain for its development.

Impact of material and energy flow variation-based iron /steel ratio on production cost

This paper establishes a model for the production cost of iron and steel enterprise.The variation rule of the production cost versus the iron/steel ratio for two cases, namely,fixed steel production and a fixed amount of molten iron,is analyzed,and the concept of a steel scrap threshold price is proposed.According to the analysis results,when the steel scrap unit price exceeds the steel scrap threshold price, an increase in the iron/steel ratio can reduce the production cost,and vice versa.When the gap between the steel scrap unit price and the steel scrap threshold price is relatively large, the impact of the iron/steel ratio on the production cost is more prominent.According to the calculation example,when steel production is fixed （284 358 t/month）and the steel scrap unit price is 263.2 yuan/t more than the steel scrap threshold price,an increase of 0.01 in the iron/steel ratio causes a monthly production cost reduction of approximately 750 000 yuan （2.63 yuan/t）.When the amount of molten iron is fixed （270 425 t/month）and the steel scrap unit price is 140.7 yuan/t more than the threshold price,an increase of 0.01 in the iron/steel ratio causes a monthly production cost reduction of approximately 430 000 yuan （1.5 yuan/t）.The results indicate that iron and steel enterprise should adjust the production strategy in time when the scrap price fluctuates, and then the production cost will be reduced.

Construction of an Evaluation Indicator System for Civic and Political Applications in Professional Practice Courses Based on CIPP:Taking the VBSE Practical Training Course as an Example

This study takes the virtual business society environment(VBSE)practical training course as a case study and applies the theoretical framework of the context,input,process,product(CIPP)model to construct an evaluation indicator system for the application of civic and politics in professional practice courses.The context evaluation is measured from the support of the VBSE practical training course into course civic and politics,teachers’cognition,and the integration of course objectives;the input evaluation is measured from the matching degree of teachers’civic and political competence,and the matching degree of teaching resources;the process evaluation is measured from the degree of implementation of civic and politics teaching and the degree of students’acceptance;and the product evaluation is measured from the degree of impact of civic and politics teaching.

Influence of mesoscale eddies on primary production in the South China Sea during spring inter-monsoon period

Mesoscale eddies have been suggested to have an impact on biological carbon fixation in the South China Sea （SCS）. However, their overall contribution to primary production during the spring inter-monsoon pe riod is still unknown. Based on large-scale biological and environmental in situ observations and synchro nous remote sensing data, the distribution patterns of phytoplankton biomass and the primary production, and the role of mesoscale eddies in regulating primary production in different eddy-controlled waters were investigated. The results suggested that the surface chlorophyll a concentrations and water column inte grated primary production （IPP） are significantly higher in cyclonic eddies and lower in the anticyclonic eddies as compared to that in non-eddy waters. Although eddies could affect various environmental factors, such as nutrients, temperature and light availability, nutrient supply is suggested to be the most important one through which mesoscale eddies regulated the distribution patterns of phytoplankton biomass and pri mary production. The estimated IPP in cyclonic and anticyclonic eddies are about 29.5% higher and 16.6% lower than the total average in the whole study area, respectively, indicating that the promotion effect of mesoscale cold eddies on the primary production was much stronger than the inhibition effect of the warm eddies per unit area. Overall, mesoscale eddies are crucial physical processes that affect the biological car bon fixation and the distribution pattern of primary production in the SCS open sea, especially during the spring inter-monsoon period.

Research on Product Information Integrating and Sharing for Dynamic Colla boration

Dynamic Collaboration emerges as the new trend of n et working and collaborating work in manufacturing industry, in which product infor mation sharing among allied enterprises plays very important roles in collaborat ing product development. This thesis aims at studying the integrating, contr olling and sharing mode of product information among the heterogeneous and dispe rsed environments through Internet, and proposes the information integrating/sha ring architecture based on the Product Master Model (PMM). The following are the main contents of this thesis: 1) Research on the XML based PMM model for integration and sharing of product in formation After analyzing the requirement of the allied Enterprise for the product infor mation, the XML based product master model (XPMM) is proposed as the integrating mechanism of heterogeneous and dispersed product information. The XPMM is divid ed into some sub-models: whole-life controlling model, product defining model, conception model, design model, product structure model, machining model, q uality model, evaluating model. The character and accessing approach of XPMM is discussed in detail. 2) Research on the mapping pattern and mapping rule of STEP/XML According to feature of XML Schema and STEP EXPRESS, the memory-constructing-t ree model is put forward as STEP/XML mapping pattern, which is constructed dynam ically according to the bottom-to-top reference relationship. Based on mapping pattern, the multi-layer XML/STEP mapping rule is discussed detailed including relation mapping, entity mapping, data type mapping, reference mapping and func tion mapping. 3) Research on the Product Information Integration and Sharing (PIIS) Architectu re Based on the XPMM, the PIIS architecture is proposed. The PIIS support the local and dispersed product information to be integrated and shared on the contro l of the XPMM. The architecture is divided into three layers :Applying-Obj ect-LayerData-Integration-Layer and STEP-Data-Layer. The kernel of the PI IS Architecture is this Data-Integration-Layer, which control the whole proces s of XPMM creating, the data approaching. The function and structure of every la yer is discussed too.

Disassemblability Modeling Technology of Configurable Product Based on Disassembly Constraint Relation Weighted Design Structure Matrix(DSM)

The current research of configurable product disassemblability focuses on disassemblability evaluation and disassembly sequence planning. Little work has been done on quantitative analysis of configurable product disassemblability. The disassemblability modeling technology for configurable product based on disassembly constraint relation weighted design structure matrix （DSM） is proposed. Major factors affecting the disassemblability of configurable product are analyzed, and the disassembling degrees between components in configurable product are obtained by calculating disassembly entropies such as joint type, joint quantity, disassembly path, disassembly accessibility and material compatibility. The disassembly constraint relation weighted DSM of configurable product is constructed and configuration modules are formed by matrix decomposition and tearing operations. The disassembly constraint relation in configuration modules is strong coupling, and the disassembly constraint relation between modules is weak coupling, and the disassemblability configuration model is constructed based on configuration module. Finally, taking a hydraulic forging press as an example, the decomposed weak coupling components are used as configuration modules alone, components with a strong coupling are aggregated into configuration modules, and the disassembly sequence of components inside configuration modules is optimized by tearing operation. A disassemblability configuration model of the hydraulic forging press is constructed. By researching the disassemblability modeling technology of product configuration design based on disassembly constraint relation weighted DSM, the disassembly property in maintenance, recycling and reuse of configurable product are optimized.

Fishery stock assessment of Kiddi shrimp (Parapenaeopsis stylifera) in the Northern Arabian Sea Coast of Pakistan by using surplus production models

Pakistani marine waters are under an open access regime. Due to poor management and policy implications, blind fishing is continued which may result in ecological as well as economic losses. Thus, it is of utmost importance to estimate fishery resources before harvesting. In this study, catch and effort data, 1996-2009, of Kiddi shrimp Parapenaeopsis stylifera fishery from Pakistani marine waters was analyzed by using specialized fishery software in order to know fishery stock status of this commercially important shrimp. Maximum, minimum and average capture production ofP. stylifera was observed as 15 912 metric tons （mr） （1997）, 9 438 mt （2009） and 11 667 mt/a. Two stock assessment tools viz. CEDA （catch and effort data analysis） and ASPIC （a stock production model incorporating covariates） were used to compute MSY （maximum sustainable yield） of this organism. In CEDA, three surplus production models, Fox, Schaefer and Pella-Tomlinson, along with three error assumptions, log, log normal and gamma, were used. For initial proportion （IP） 0.8, the Fox model computed MSY as 6 858 nat （CV=0.204, R^2=0.709） and 7 384 mt （CV=0.149, R^2=0.72） for log and log normal error assumption respectively. Here, gamma error produced minimization failure. Estimated MSY by using Schaefer and Pella-Tomlinson models remained the same for log, log normal and gamma error assumptions i.e. 7 083 mt, 8 209 mt and 7 242 mt correspondingly. The Schafer results showed highest goodness of fit R2 （0.712） values. ASPIC computed MSY, CV, R2, FMsv and BMsv parameters for the Fox model as 7 219 nat, 0.142, 0.872, 0.111 and 65 280, while for the Logistic model the computed values remained 7 720 mt, 0.148, 0.868, 0.107 and 72 110 correspondingly. Results obtained have shown that P. stylifera has been overexploited. Immediate steps are needed to conserve this fishery resource for the future and research on other species of commercial importance is urgently needed.

Assessing the Fishery Resource Status of China’s Coastal Waters Using Surplus Production Models

Surplus production models(SPMs)are among the simplest and most widely used fishery stock assessment models.The catch-effort data analysis(CEDA)and a surplus production model incorporating covariates(ASPIC)are softwares for analyzing fishery catch and fishing effort data using nonequilibrium SPMs.In China Fishery Statistical Yearbook,annual fishery production and fishing effort data of the Yellow Sea,Bohai Sea,East China Sea,and South China Sea have been published from 1979 till present.Using its catch and fishing effort data from 1980 to 2018,we apply the CEDA and ASPIC to evaluate fishery resources in Chinese coastal waters.The results show that the total maximum sustainable yield(MSY)estimate of the four China seas is 10.05-10.83 million tons,approximately equal to the marine fishery catch(10.44 million tons)reported in 2018.It can be concluded that China’s coastal fishery resources are currently fully exploited and must be protected with a precautionary approach.Both softwares produced similar results;however,the CEDA had a much higher R2 value(above 0.9)than ASPIC(about 0.2),indicating that CEDA can better fit the data and therefore is more suitable for analyzing the fishery resources in the coastal waters of China.

A stock assessment for Illex argentinus in Southwest Atlantic using an environmentally dependent surplus production model

The southern Patagonian stock（SPS） of Argentinian shortfin squid, Illex argentinus, is an economically important squid fishery in the Southwest Atlantic. Environmental conditions in the region play an important role in regulating the population dynamics of the I. argentinus population. This study develops an environmentally dependent surplus production（EDSP） model to evaluate the stock abundance of I. argentines during the period of 2000 to 2010. The environmental factors（favorable spawning habitat areas with sea surface temperature of 16–18°C） were assumed to be closely associated with carrying capacity（K） in the EDSP model. Deviance Information Criterion（DIC） values suggest that the estimated EDSP model with environmental factors fits the data better than a Schaefer surplus model without environmental factors under uniform and normal scenarios.The EDSP model estimated a maximum sustainable yield（MSY） from 351 600 t to 685 100 t and a biomass from 1 322 400 t to1 803 000 t. The fishing mortality coefficient of I. argentinus from 2000 to 2010 was smaller than the values of F（0.1） and F（MSY）. Furthermore, the time series biomass plot of I. argentinus from 2000 to 2010 shows that the biomass of I.argentinus and this fishery were in a good state and not presently experiencing overfishing. This study suggests that the environmental conditions of the habitat should be considered within squid stock assessment and management.

Forecasting of China's natural gas production and its policy implications

With the vigorous promotion of energy conservation and implementation of clean energy strategies,China＇s natural gas industry has entered a rapid development phase,and natural gas is playing an increasingly important role in China＇s energy structure.This paper uses a Generalized Weng model to forecast Chinese regional natural gas production,where accuracy and reasonableness compared with other predictions are enhanced by taking remaining estimated recoverable resources as a criterion.The forecast shows that China＇s natural gas production will maintain a rapid growth with peak gas of 323 billion cubic meters a year coming in 2036;in 2020,natural gas production will surpass that of oil to become a more important source of energy.Natural gas will play an important role in optimizing China＇s energy consumption structure and will be a strategic replacement of oil.This will require that exploration and development of conventional natural gas is highly valued and its industrial development to be reasonably planned.As well,full use should be made of domestic and international markets.Initiative should also be taken in the exploration and development of unconventional and deepwater gas,which shall form a complement to the development of China＇s conventional natural gas industry.

Long-term organic and inorganic fertilizations enhanced basic soil productivity in a fluvo-aquic soil

The improvement of soil productivity depends on a rational input of water and nutrients, optimal field management, and the increase of basic soil productivity（BSP）. In this study, BSP is defined as the productive capacity of a farmland soil with its own physical and chemical properties for a specific crop season under local field management. Based on 19-yr data of the long-term agronomic experiments（1989–2008） on a fluvo-aquic soil in Zhengzhou, Henan Province, China, the decision support system for agrotechnology transfer（DSSAT ver. 4.0） crop growth model was used to simulate yields by BSP of winter wheat（Triticum aestivium L.） and summer maize（Zea mays L.） to examine the relationship between BSP and soil organic carbon（SOC） under long-term fertilization. Five treatments were included：（1） no fertilization（control）,（2） nitrogen, phosphorus and potassium fertilizers（NPK）,（3） NPK plus manure（NPKM）,（4） 1.5 times of NPKM（1.5NPKM）, and（5） NPK plus straw（NPKS）. After 19 yr of treatments, the SOC stock increased 16.7, 44.2, 69.9, and 25.2% under the NPK, NPKM, 1.5NPKM, and NPKS, respectively, compared to the initial value. Among various nutrient factors affecting contribution percentage of BSP to winter wheat and summer maize, SOC was a major affecting factor for BSP in the fluvo-aquic soil. There were significant positive correlations between SOC stock and yields by BSP of winter wheat and summer maize（P〈0.01）, and yields by BSP of winter wheat and summer maize increased 154 and 132 kg ha^（–1） when SOC stock increased 1 t C ha^（–1）. Thus, increased SOC accumulation is a crucial way for increasing BSP in fluvo-aquic soil. The manure or straw combined application with chemical fertilizers significantly enhanced BSP compared to the application of chemical fertilizers alone.

Construction of Agricultural Tourism Product Model Based on Experience Economy

Experience economy is a new economic development tendency after agricultural economy, industrial economy and service economy. Tourism consumption shows new characteristics in experience economy. Agricultural tourism product coincides with these characteristics, it is necessary to establish a model of agricultural tourism products based on experience economy. It is a model of wide range, strong personality and participation.

Research Advances in Net Primary Productivity of Terrestrial Ecosystem

The net primary productivity of vegetation reflects the total amount of carbon fixed by plants through photosynthesis each year. The study of vegetation net primary productivity is one of the core contents of global change and terrestrial ecosystems. This article reviews the current research status of net primary productivity of terrestrial vegetation, and comprehensively analyzes the advantages and disadvantages of three types of productivity estimation models, climate relative models, biogeochemical models, and light energy utilization models. The light energy utilization models have become the mainstream method for estimating vegetation net primary productivity because they can directly use remote sensing data. However, there are still many deficiencies in the estimation of vegetation net primary productivity, which need to be further improved and tested.

HEURISTIC MODELING FOR A DYNAMIC AND GOAL PROGRAMMING IN PRODUCTION PLANNING OF CONTINUOUS MANUFACTURING SYSTEMS

At the first sight it seems that advanced operation research is not used enough in continuous production systems as comparison with mass production, batch production and job shop systems, but really in a comprehensive evaluation the advanced operation research techniques can be used in continuous production systems in developing countries very widely, because of initial inadequate plant layout, stage by stage development of production lines, the purchase of second hand machineries from various countries, plurality of customers. A case of production system planning is proposed for a chemical company in which the above mentioned conditions are almost presented. The goals and constraints in this issue are as follows： （1） Minimizing deviation of customer＇s requirements. （2） Maximizing the profit. （3） Minimizing the frequencies of changes in formula production. （4） Minimizing the inventory of final products. （5） Balancing the production sections with regard to rate in production. （6） Limitation in inventory of raw material. The present situation is in such a way that various techniques such as goal programming, linear programming and dynamic programming can be used. But dynamic production programming issues are divided into two categories, at first one with limitation in production capacity and another with unlimited production capacity. For the first category, a systematic and acceptable solution has not been presented yet. Therefore an innovative method is used to convert the dynamic situation to a zero- one model. At last this issue is changed to a goal programming model with non-linear limitations with the use of GRG algorithm and that＇s how it is solved.