Cost Minimization Is Essential For The Sustainable Development Of An Industry: A Mathematical Economic Model Approach

The method of Lagrange multiplier is a very useful and powerful technique in multivariable calculus. In this study, interpretation of Lagrange multiplier is given with satisfactory mathematical calculations and shows that its value is positive. For the sustainable development of an industry, cost minimization policy is crucial. In any industry, the main objective is to minimize production cost for maximizing its profit. By considering Lagrange multiplier technique application an attempt has been taken here in cost minimization problem subject to production function as an output constraint. To predict future performance of an industry, mathematical calculations are necessary and all the procedures are given in this paper with detail mathematical procedures. In this study, an attempt has been taken to minimize cost by considering three variables capital, labour, and other inputs of an industry by the application of economic models subject to a budget constraint, using Lagrange multiplier technique, as well as, using necessary and sufficient conditions for minimum value.