[01] Haradhan Kumar Mohajan, Department of Mathematics, Premier University, Chittagong, Bangladesh.

Every factory wants to obtain a maximum production that provides a maximum profit, and also wants to go ahead with a sustainable way in the competitive global economy. To achieve a sustainable economic environment, the factory must run in ensuing scientific methods. This study has considered three inputs, such as capital, labor and other inputs for the sustainable production of the factory. In this article, the economic predictions are given by the comparative statics with detail mathematical analysis. Bangladesh is a developing country in the South Asia. It is densely populated country but short of skilled workforce. Agriculture is the principal sector of its economy. Only depending on agriculture sector a country cannot reach its economic peak. Recently, Bangladesh moves to industrialization. To increase national wealth and fortune, the country must produce high quality of products and needs to export surplus products in global markets. So, the production sector of the country has to increase production depending on the local and global demands. For a long-term sustainable production it must run the factories efficiently and future production techniques should be in scientific based. In this study an attempt has been taken to maximize products of a factory of Bangladesh subject to a budget constraint, using Lagrange multiplier technique, as well as, applying necessary and sufficient conditions to achieve optimal result.

Bangladesh, Lagrange Multiplier, Product Maximization, Sustainability

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