10/28: Constrained optimization and Lagrange multipliers

1. Main Points

In todays reading I learned how to solve a constrained optimization problem using Lagrange multipliers and Lagrange functions. A lagrange multiplier is an approximation of the change in the optimum value of f when the value of the constraint is increased by 1 unit. In terms of production, it can be seen as the “extra bang for your buck”. Lagranges multiplier is calculated by taking the function to be optimized over the constraining function. Lagrangian functions are used when dealing with constrained optimization problems by first writing down the Lagrangian function and then finding the critical points of the Langrangian Function.

2. Challenging

I did not quite understand why we find the critical points of the Lagrangian function when solving constrained optimization problems nor what they represent.

3. Intriguing

The Lagrangian multiplier and function must be immensely useful when doing calculations for business management. Now I understand what the basis for the expression “getting the most bang for your buck” is!