1. Lagrange Multipliers

2. Objective: -Understand the method of Lagrange multipliers -Use Lagrange multipliers to solve constrained optimization problems (functions of two variables)

3. Finding Relative extreme is easy (inside the region) Absolute extreme is long and messy because of the boundary condition So what???

4. Example: Let’s say we want to find a rectangle of maximum area which can be inscribed in the ellipse given by

5. What can you say about the gradients of the functions f and g at the intersection point?

6. Lagrange's Theorem

8. What is the use of this Lagrange Multipliers?

9. Method of Lagrange Multipliers

10. Let’s continue the example

11. Example to Try

12. Try Me and get rest

13. Home work