SurCalCh7Sec5 - Lagrange Multipliers Sometimes we need to...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Lagrange Multipliers Sometimes we need to optimize functions subject to some constraint. To solve such constrained optimization problems we use the method of Lagrange Multipliers To optimize subject to : ) , ( y x f 0 ) , ( = y x g 1) Write the new function =+ ) , , ( λ y x F ) , ( y x g , ( y x f ) 2) Find F , , and and set them all equal to zero. Solve this system to find the critical points. x y F F To solve this system it is often helpful to solve and for . Set those two expressions for equal to each other and use the result with to find x and y. 0 = x F 0 = y F 0 = F 3) The solution to the original problem (if it exists) will occur at one of these critical points Note: This method only finds the critical points, it does not tell whether the function is maximized, minimized or neither at the critical
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/12/2012 for the course MATH 2043 taught by Professor Pamelasatterfield during the Fall '05 term at NorthWest Arkansas Community College.

Ask a homework question - tutors are online