• Priyansh Lodha

The objective of this study is to utilize multivariable calculus to optimize the x (capital) and y (labour) variables in the context of a production function. This will be achieved by identifying the point of intersection between the Production Quantity Function & Cost Function, at a predetermined production level. Subsequently, the research will expand on this analysis by incorporating a cost constraint function in order to optimize production levels within the constraints of a specified budget. This approach accounts for the reality that many businesses have financial limitations on their investment capabilities. For the purpose of illustrating the generalised equations, I have used the financial data of an American public limited company - Ecolab Inc. I have calculated the optimal combination of input levels for profit maximization based on the interpolated data to obtain a product function.

Profit maximisation, Multivariable optimisation, calculus, Cobb Douglas Product Function, Two Factor Cobb-Douglas Function

"DETERMINING THE PROFIT MAXIMISATION INPUT LEVELS OF ECOLAB INC. USING MULTIVARIABLE OPTIMIZATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 7, page no.g647-g663, July-2023, Available :http://www.jetir.org/papers/JETIR2307687.pdf

"DETERMINING THE PROFIT MAXIMISATION INPUT LEVELS OF ECOLAB INC. USING MULTIVARIABLE OPTIMIZATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 7, page no. ppg647-g663, July-2023, Available at : http://www.jetir.org/papers/JETIR2307687.pdf