Economic Investigation of Lagrange Multiplier if Cost of Inputs and Budget Size of a Firm Increase: A Profit Maximization Endeavor

Mohajan, Devajit and Mohajan, Haradhan (2023): Economic Investigation of Lagrange Multiplier if Cost of Inputs and Budget Size of a Firm Increase: A Profit Maximization Endeavor. Published in: Annals of Spiru Haret University. Economic Series , Vol. 23, No. 2 (10 July 2023): pp. 340-364.

Abstract

In this study method of Lagrange multiplier is considered to investigate profit maximization policy. In the twenty first century global economy faces serious complexities. Sensitivity analysis of economic firms becomes essential part of sustainable economic environment. The method of Lagrange multiplier is a very useful and powerful technique in multivariable calculus that is applied in economic models to obtain higher dimensional unconstrained problem from the lower dimensional constrained problems. This paper proceeds with Cobb-Douglas production function, where 6×6 bordered Hessian and 6×6 Jacobian are used to examine sensitivity analysis efficiently and elaborately.

• Item Type: MPRA Paper
• Language: English
• Keywords: Budget, inputs, Lagrange multiplier, profit maximization
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C38 - Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models; J - Labor and Demographic Economics > J3 - Wages, Compensation, and Labor Costs

References

Baxley, J. V., & Moorhouse, J. C. (1984). Lagrange Multiplier Problems in Economics. The American Mathematical Monthly, 91(7), 404-412.

Carter, M. (2001). Foundations of Mathematical Economics. MIT Press, Cambridge, London.

Cobb, C. W., & Douglass, P. H. (1928). A Theory of Production. American Economics Review, 18(1), 139-165.

Dixit, A. K. (1990). Optimization in Economic Theory (2nd Ed.). Oxford University Press, Oxford.

Das, S., & Mohajan, H. K. (2014a). Generating Function for M(m,n). Turkish Journal of Analysis and Number Theory, 2(4), 125-129.

Das, S., & Mohajan, H. K. (2014b). Development of Partition Functions of Ramanujan’s Works. Journal of Environmental Treatment Techniques, 2(4), 143-149.

Datta, R., & Mohajan, H. K. (2013a). Financial Intermediaries in Development of Capital Market in Bangladesh. Lambert Academic Publishing, Germany.

Datta, R., & Mohajan, H. K. (2013b). Home Loan Repayment Performance in Bangladesh. Lambert Academic Publishing, Germany.

Datta, R., Chowdhury, T. U., & Mohajan, H. K. (2013). Reassess of Capital Structure Theories. International Journal of Research in Computer Application & Management, 3(10), 102–106.

Eaton, B., & Lipsey, R. (1975). The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition. Review of Economic Studies, 42(1), 27-49.

Ferdous, J., & Mohajan, H. K. (2022). Maximum Profit Ensured for Industry Sustainability. Annals of Spiru Haret University. Economic Series, 22(3), 317-337.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2009a). Preference of Social Choice in Mathematical Economics. Indus Journal of Management & Social Sciences, 3(1), 17-38.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2009b). Political Economy and Social Welfare with Voting Procedure. KASBIT Business Journal, 2(1), 42-66.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2010). Utility Maximization Subject to Multiple Constraints. Indus Journal of Management & Social Sciences, 4(1), 15-29.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2011). Output Maximization Subject to a Nonlinear Constraint. KASBIT Business Journal, 4(1), 116-128.

Legesse, B. (2014). Research Methods in Agribusiness and Value Chains. School of Agricultural Economics and Agribusiness, Haramaya University.

Mohajan, D., & Mohajan, H. K. (2022a). Mathematical Analysis of SEIR Model to Prevent COVID-19 Pandemic. Journal of Economic Development, Environment and People, 11(4), 5-30.

Mohajan, D., & Mohajan, H. K. (2022b). Utility Maximization Analysis of an Emerging Firm: A Bordered Hessian Approach. Annals of Spiru Haret University. Economic Series, 22(4), 292-308.

Mohajan, D., & Mohajan, H. K. (2022c). Sensitivity Analysis among Commodities and Coupons during Utility Maximization. Frontiers in Management Science, 1(3), 13-28.

Mohajan, D., & Mohajan, H. K. (2022d). Importance of Total Coupon in Utility Maximization: A Sensitivity Analysis. Law and Economy, 1(5), 65-67.

Mohajan, D., & Mohajan, H. K. (2022e). Development of Grounded Theory in Social Sciences: A Qualitative Approach. Studies in Social Science & Humanities, 1(5), 13-24.

Mohajan, D., & Mohajan, H. K. (2022f). Exploration of Coding in Qualitative Data Analysis: Grounded Theory Perspective. Research and Advances in Education, 1(6), 50-60.

Mohajan, D., & Mohajan, H. K. (2022g). Memo Writing Procedures in Grounded Theory Research Methodology. Studies in Social Science & Humanities, 1(4), 10-18.

Mohajan, D., & Mohajan, H. K. (2022h). Constructivist Grounded Theory: A New Research Approach in Social Science. Research and Advances in Education, 1(4), 8-16.

Mohajan, D., & Mohajan, H. K. (2022i). Feminism and Feminist Grounded Theory: A Comprehensive Research Analysis. Journal of Economic Development, Environment and People, 11(3), 49-61.

Mohajan, D., & Mohajan, H. K. (2022j). Profit Maximization Strategy in an Industry: A Sustainable Procedure. Law and Economy, 1(3), 17-43.

Mohajan, D., & Mohajan, H. K. (2023a). Sensitivity Analysis among Commodities and Prices: Utility Maximization Perceptions. Law and Economy, 2(2), 1-16.

Mohajan, D., & Mohajan, H. K. (2023b). Straussian Grounded Theory: An Evolved Variant in Qualitative Research. Studies in Social Science & Humanities, 2(2), 33-40.

Mohajan, D., & Mohajan, H. K. (2023c). Sensitivity Analysis between Lagrange Multipliers and Consumer Coupon: Utility Maximization Perspective. Frontiers in Management Science, 2(1), 14-25.

Mohajan, D., & Mohajan, H. K. (2023d). Utility Maximization Analysis of an Organization: A Mathematical Economic Procedure. Law and Economy, 2(1), 1-15.

Mohajan, D., & Mohajan, H. K. (2023e). Classic Grounded Theory: A Qualitative Research on Human Behavior. Studies in Social Science & Humanities, 2(1), 1-7.

Mohajan, D., & Mohajan, H. K. (2023f). Sensitivity Analysis between Commodity and Budget: Utility Maximization Case. Law and Economy, 2(3), 10-21.

Mohajan, D., & Mohajan, H. K. (2023g). Sensitivity Analysis for Profit Maximization with Respect to Per Unit Cost of Subsidiary Raw Materials. Frontiers in Management Science, 2(2), 13-27.

Mohajan, D., & Mohajan, H. K. (2023h). Families of Grounded Theory: A Theoretical Structure for Novel Researchers. Studies in Social Science & Humanities, 2(1), 56-65.

Mohajan, D., & Mohajan, H. K. (2023i). Broca Index: A Simple Tool to Measure Ideal Body Weight. Innovation in Science and Technology, 2(2), 21-24.

Mohajan, D., & Mohajan, H. K. (2023j). Obesity and Its Related Diseases: A New Escalating Alarming in Global Health. Journal of Innovations in Medical Research, 2(3), 12-23.

Mohajan, D., & Mohajan, H. K. (2023k). A Study on Body Fat Percentage for Physical Fitness and Prevention of Obesity: A Two Compartment Model. Journal of Innovations in Medical Research, 2(4), 1–10.

Mohajan, D., & Mohajan, H. K. (2023l). Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration. Law and Economy, 2(4), 32-48.

Mohajan, D., & Mohajan, H. K. (2023m). Ponderal Index: An Important Anthropometric Indicator for Physical Growth. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023n). Long-Term Regular Exercise Increases V̇O2max for Cardiorespiratory Fitness. Innovation in Science and Technology, 2(2), 38-43.

Mohajan, D., & Mohajan, H. K. (2023o). Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case. Annals of Spiru Haret University. Economic Series, 23(1), 167-185.

Mohajan, D., & Mohajan, H. K. (2023p). Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science. Journal of Economic Development, Environment and People, 12(1), 72-81.

Mohajan, D., & Mohajan, H. K. (2023q). Economic Situations of Lagrange Multiplier When Costs of Various Inputs Increase for Nonlinear Budget Constraint. Studies in Social Science & Humanities, 2(4), 40-64.

Mohajan, D., & Mohajan, H. K. (2023r). Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons. Journal of Economic Development, Environment, and People, 12(1), 25-40.

Mohajan, D., & Mohajan, H. K. (2023s). Anorexia Nervosa: A Dreadful Psychosocial Health Complication. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023t). Bulimia Nervosa: A Psychiatric Problem of Disorder. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023u). Binge-Eating: A Life-Threatening Eating Disorder. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023v). Panniculus Morbidus: A New Global Health Crisis Due to Extreme Obesity. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023w). Abdominal Elephantiasis: An Obstructive Disease Due to Extreme Obesity. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023x). Bulimia Nervosa: A Psychiatric Problem of Disorder. Innovation in Science and Technology, 2(3), 26-32.

Mohajan, D., & Mohajan, H. K. (2023y). A Study on Nonlinear Budget Constraint of a Local Industrial Firm of Bangladesh: A Profit Maximization Investigation. Law and Economy, 2(5), 27-33.

Mohajan, D., & Mohajan, H. K. (2023z). Mathematical Model for Nonlinear Budget Constraint: Economic Activities on Increased Budget. Studies in Social Science & Humanities, 2(5), 20-40.

Mohajan, D., & Mohajan, H. K. (2023A). Body Mass Index (BMI) is a Popular Anthropometric Tool to Measure Obesity among Adults. Journal of Innovations in Medical Research, 2(4), 25-33.

Mohajan, D., & Mohajan, H. K. (2023B). Ponderal Index: An Important Anthropometric Indicator for Physical Growth. Journal of Innovations in Medical Research, 2(6), 15–19.

Mohajan, D., & Mohajan, H. K. (2023C). An Economical Study When Cost of Irregular Raw Materials of an Industry Increases for Nonlinear Budget Constraint. Law and Economy, 2(7), 24–43.

Mohajan, D., & Mohajan, H. K. (2023D). Historical View of Diabetics Mellitus: From Ancient Egyptian Polyuria to Discovery of Insulin. Studies in Social Science & Humanities, 2(7), 26–34.

Mohajan, D., & Mohajan, H. K. (2023E). Effects of Various Inputs for Increased Interest Rate of Capital: A Nonlinear Budget Constraint Consideration. Frontiers in Management Science, 2(4), 15–33.

Mohajan, D., & Mohajan, H. K. (2023F). Various Problems Arise in Industrial Economics If Wage Rate Increases: A Study for Nonlinear Budget Constraint. Law and Economy, 2(6), 1–19. Mohajan, D., & Mohajan, H. K. (2023G). Economic Aspects of Profit Maximization if Cost of Principal Raw Material Increases. Frontiers in Management Science, 2(3), 28–42.

Mohajan, H. K. (2011a). The NNP and Sustainability in Open Economy: Highlights on Recent World Economy and on Open Economy of Bangladesh. KASBIT Business Journal, 4(2), 32-47.

Mohajan, H. K. (2011b). Optimal Environmental Taxes Due to Health Effect. KASBIT Business Journal, 4(1), 1-19.

Mohajan, H. K. (2011c). The Real Net National Product in Sustainable Development. KASBIT Business Journal, 4(2), 90-103.

Mohajan, H. K. (2011d). Approval Voting: A Multi-outcome Election. KASBIT Business Journal, 4(2), 77–88.

Mohajan, H. K. (2012b). Aspects of Green Marketing: A Prospect for Bangladesh. International Journal of Economics and Research, 3(3), 1-11.

Mohajan, H. K. (2012c). Importance of Green Marketing at Present and Future. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2012d). Greenhouse Gas Emissions of the USA. Indus Journal of Management & Social Sciences, 6(2), 132-148.

Mohajan, H. K. (2012e). Relation between Lease Finance and Purchase. International Journal of Economics and Research, 3(3), 146-158.

Mohajan, H. K. (2012f). Air Pollution Causes Health Effects and Net National Product of a Country Decreases: A Theoretical Framework. International Journal of Development Research and Quantitative Techniques, 2(2), 3-10.

Mohajan, H. K. (2012g). Social Welfare and Social Choice in Different Individuals’ Preferences. International Journal of Human Development and Sustainability, 5(1), 11-22.

Mohajan, H. K. (2012h). Valuing Health Impacts of the Workers in Bangladesh Due to Air Pollution. International Journal of Economics and Research, 3(1), 123-132.

Mohajan, H. K. (2012i). Single Transferable Vote in Local and National Elections. International Journal of Strategic Organization and Behavioural Science, 2(2), 3-18.

Mohajan, H. K. (2012j). The Lease Financing in Bangladesh: A Satisfied Progress in Business and Industrialization. International Journal of Finance and Policy Analysis, 4(1), 9-24.

Mohajan, H. K. (2013a). Economic Development of Bangladesh. Journal of Business Management and Administration, 1(4), 41-48.

Mohajan, H. K. (2013b). Ethiopia: A Socio-economic Study. Journal of Business Management and Administration, 1(5), 59-74.

Mohajan, H. K. (2013c). Friedmann, Robertson-Walker (FRW) Models in Cosmology. Journal of Environmental Treatment Techniques, 1(3), 158-164.

Mohajan, H. K. (2013d). Global Greenhouse Gas Emissions and Climate Change. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2013e). Global Food Price Hike is a Burden to the Poor. International Journal of Information Technology and Business Management, 19(1), 1-15.

Mohajan, H. K. (2013f). Food, Agriculture and Economic Situation of Bangladesh. Proceedings of 2nd International Conference on Global Sustainable Development (2nd ICGSD-2013), held on 05-06, October, 2013. Khadim Ali Shah Bukhari Institute of Technology (KASBIT). MPRA Paper No. 54240.

Mohajan, H. K. (2013g). Greenhouse Gas Emissions from Small Industries and its Impact on Global Warming. KASBIT Business Journal, 6(1&2), 1-13.

Mohajan, H. K. (2013h). Violation of Human Rights in Bangladesh. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2013i). Net National Product and Sustainability. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2013j). An Introduction to Voting System. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2013l). Environmental Taxes for the Improvement of Health. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2013k). Declining Economy in Zambia and its Impact in Food Security. Peak Journal of Food Science and Technology, 1(3), 27-34.

Mohajan, H. K. (2014a). Greenhouse Gas Emissions of China. Journal of Environmental Treatment Techniques, 1(4), 190-202.

Mohajan, H. K. (2014b). Chinese Sulphur Dioxide Emissions and Local Environment Pollution. International Journal of Scientific Research in Knowledge, 2(6), 265-276.

Mohajan, H. K. (2014c). The Most Fatal 2014 Outbreak of Ebolavirus Disease in Western Africa. American Journal of Epidemiology and Infectious Disease, 2(4), 101-108.

Mohajan, H. K. (2014d). Improvement of Health Sector in Kenya. American Journal of Public Health Research, 2(4), 159-169.

Mohajan, H. K. (2014e). Food and Nutrition of Bangladesh. Peak Journal of Food Science and Technology, 2(1), 1-17.

Mohajan, H. K. (2014f). An Introduction to Business. Open Science Book Publishing, The USA.

Mohajan, H. K. (2014g). Food and Economics of the Poor. Open Science Book Publishing, The USA.

Mohajan, H. K. (2015a). Sustainable Development Policy of Global Economy. American Journal of Environmental Protection, 3(1), 12-29.

Mohajan, H. K. (2015b). Present and Future of Nestlé Bangladesh Limited. American Journal of Food and Nutrition, 3(2), 34-43.

Mohajan, H. K. (2015c). Basic Concepts of Differential Geometry and Fibre Bundles. ABC Journal of Advanced Research, 4(1), 57-73.

Mohajan, H. K. (2015d). Tuberculosis is a Fatal Disease among Some Developing Countries of the World. American Journal of Infectious Diseases and Microbiology, 3(1), 18-31.

Mohajan, H. K. (2016a). An Analysis of Knowledge Management for the Development of Global Health. American Journal of Social Sciences, 4(4), 38-57.

Mohajan, H. K. (2016b). Amartya Sen’s Peasant Economies: A Review with Examples. Open Access Library Journal, 3, e2337, 1-15.

Mohajan, H. K. (2017a). Roles of Communities of Practice for the Development of the Society. Journal of Economic Development, Environment and People, 6(3), 27-46.

Mohajan, H. K. (2017b). Optimization Models in Mathematical Economics. Journal of Scientific Achievements, 2(5), 30-42.

Mohajan, H. K. (2017c). A Brief Analysis of de Sitter Universe in Relativistic Cosmology. Journal of Scientific Achievements, 2(11), 1-17.

Mohajan, H. K. (2017d). Analysis of Reciprocity and Substitution Theorems, and Slutsky Equation. Noble International Journal of Economics and Financial Research, 2(3), 54-75.

Mohajan, H. K. (2017e). Research Methodology. Aspects of Mathematical Economics, Social Choice and Game Theory, PhD Thesis. Munich Personal RePEc Archive, 10, 1-20.

Mohajan, H. K. (2017f). The Nature of Naked Singularity in Cosmology. Engineering International, 5(1), 9-26.

Mohajan, H. K. (2018a). Aspects of Mathematical Economics, Social Choice and Game Theory. PhD Dissertation, Jamal Nazrul Islam Research Centre for Mathematical and Physical Sciences (JNIRCMPS), University of Chittagong, Chittagong, Bangladesh.

Mohajan, H. K. (2018b). The Rohingya Muslims in Myanmar are Victim of Genocide! ABC Journal of Advanced Research, 7(1), 59-72.

Mohajan, H. K. (2018c). Medical Errors Must be Reduced for the Welfare of the Global Health Sector. International Journal of Public Health and Health Systems, 3(5), 91-101.

Mohajan, H. K. (2018d). Analysis of Food Production and Poverty Reduction of Bangladesh. Annals of Spiru Haret University Economic Series, 18(1), 191-205.

Mohajan, H. K. (2019). The First Industrial Revolution: Creation of a New Global Human Era. Journal of Social Sciences and Humanities, 5(4), 377-387.

Mohajan, H. K. (2020a). Quantitative Research: A Successful Investigation in Natural and Social Sciences. Journal of Economic Development, Environment and People, 9(4), 50-79.

Mohajan, H. K. (2020b). COVID-19–The Most Fatal Pandemic Outbreak: An Analysis of Economic Consequences. Annals of Spiru Haret University Economic Series, 20(2), 127-146.

Mohajan, H. K. (2020c). The COVID-19 in Italy: Remedies to Reduce the Infections and Deaths. Malaysian Journal of Medical and Biological Research, 7(2), 59-66.

Mohajan, H. K. (2020d). Most Fatal Pandemic COVID-19 Outbreak: An Analysis of Economic Consequences. Annals of Spiru Haret University Economic Series, 20(2), 127-146.

Mohajan, H. K. (2020e). Circular Economy can Provide a Sustainable Global Society. Journal of Economic Development, Environment and People, 9(3), 38-62.

Mohajan, H. K. (2020f). The Second Industrial Revolution has Brought Modern Social and Economic Developments. Journal of Social Sciences and Humanities, 6(1), 1-14.

Mohajan, H. K. (2021a). Aspects of Global COVID-19 Pandemic. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2021b). Global COVID-19 Pandemic: Prevention and Protection Techniques. Journal of Economic Development, Environment and People, 10(1), 51-72.

Mohajan, H. K. (2021c). Estimation of Cost Minimization of Garments Sector by Cobb-Douglass Production Function: Bangladesh Perspective. Annals of Spiru Haret University. Economic Series, 21(2), 267-299.

Mohajan, H. K. (2021d). Product Maximization Techniques of a Factory of Bangladesh: A Sustainable Procedure. American Journal of Economics, Finance and Management, 5(2), 23-44.

Mohajan, H. K. (2021e). Third Industrial Revolution Brings Global Development. Journal of Social Sciences and Humanities, 7(4), 239-251.

Mohajan, H. K. (2021f). Space-Time Singularities in Cosmology Due to Gravitation. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2021g). Circular Economy in China: Towards the Progress. International Journal of Economics and Business Administration, 7(3), 89-96.

Mohajan, H. K. (2021h). Germany is Ahead to Implement Sustainable Circular Economy. Journal of Economic Development, Environment and People, 10(2), 46-64.

Mohajan, H. K. (2022a). Four Waves of Feminism: A Blessing for Global Humanity. Studies in Social Science & Humanities, 1(2), 1-8.

Mohajan, H. K. (2022b). An Overview on the Feminism and Its Categories. Research and Advances in Education, 1(3), 11-26.

Mohajan, H. K. (2022c). Cost Minimization Analysis of a Running Firm with Economic Policy. Annals of Spiru Haret University. Economic Series, 22(3), 317-337.

Mohajan, H. K. (2022d). Mathematical Analysis of SIR Model for COVID-19 Transmission. Journal of Innovations in Medical Research, 1(2), 1-18.

Mohajan, H. K. (2022e). Food Insecurity and Malnutrition of Africa: A Combined Attempt Can Reduce Them. Journal of Economic Development, Environment and People, 11(1), 24-34.

Mohajan, H. K., & Datta, R. (2013). Stress Management Policy. Lambert Academic Publishing, Germany.

Mohajan, H. K., & Datta, R. (2012). Capital Budgeting for Foreign Direct Investment: Bangladesh Overview. Lambert Academic Publishing, Germany.

Mohajan, H. K., Datta, R., & Das, A. K. (2012). Emerging Equity Market and Economic Development: Bangladesh Perspective. International Journal of Economics and Research, 3(3), 128-145.

Mohajan, H. K., Islam, J. N., & Moolio, P. (2013). Optimization and Social Welfare in Economics. Lambert Academic Publishing, Germany.

Moolio, P., Islam, J. N., & Mohajan, H. K. (2009). Output Maximization of an Agency. Indus Journal of Management and Social Sciences, 3(1), 39-51.

Ojo, S. O. (2003). Productivity and Technical Efficiency of Poultry Egg Production in Nigeria. International Journal of Poultry Science, 2(6), 459-464.

Pandey, P., & Pandey, M. M. (2015). Research Methodology: Tools and Techniques. Bridge Center, Romania, European Union.

Polit, D. F., & Hungler, B. P. (2013). Essentials of Nursing Research: Methods, Appraisal, and Utilization (8th Ed.). Philadelphia: Wolters Kluwer/Lippincott Williams and Wilkins.

Remenyi, D. S. J., Swartz, E., Money, A., & Williams, B. (1998). Doing Research in Business and Management: An Introduction to Process and Method. SAGE Publications, London.

Rahman, M. M., & Mohajan, H. K. (2019). Rohingya-The Stateless Community Becoming the Lost Generation. Journal of Economic Development, Environment and People, 8(2), 24-36.

Rahman, M. M., & Mohajan, H. K., & Bose, T. K. (2021). Future of Rohingyas: Dignified Return to Myanmar or Restoring Their Rights or Both. The Indonesian Journal of Southeast Asian Studies, 4(2), 145-170.

Roy, L., Molla, R., & Mohajan, H. K. (2021). Cost Minimization is Essential for the Sustainability of an Industry: A Mathematical Economic Model Approach. Annals of Spiru Haret University Economic Series, 21(1), 37-69.

Samuelson, P. A. (1947). Foundations of Economic Analysis. Harvard University Press, Cambridge, MA.

Zhao, Q., Zhang, Y., & Friedman, D. (2017). Multi-Product Utility Maximization for Economic Recommendation. WSDM, 435-443.