Applications of Lagrange Multiplier in Economics or Computer Science

Question

I'm a high school student studying grade 12 maths and I need to write a 12 page paper on the Lagrange Multiplier. I have understood the mathematics behind it but I need a real equation or application of this concept which one can observe in the real world. Like an equation which has been derived from a company's revenue or something like that. This is required since I need to incorporate the use of mathematics to a real-life situation. If you cannot think of any equations right off the top of your head, could you please suggest methods to derive the equation using data? Any type of help is very much appreciated.

Thank you

Answer 1

Used in Machine learning for minimizing Cost function. This one is for SVM(Support Vector Machine) http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/stfhtmlnode64.html

Answer 2

Lagrange multipliers are used to solve problems where you are trying to minimize or maximize something subject to constraints.

For example, maximize profits subject to an initial investment of $10000.

Another example, minimize risk subject to a likely profit of 20%.

Another example, maximize production yield subject to raw materials of XXX amount.

They keywords here are “constrained optimization”. If you look for that, you’ll find a gazillion applications.