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 : ),(yxf0),(=yxg1) Write the new function =+),,(λyxF),(yxg,(yxf)2) Find F, , and and set them all equal to zero. Solve this system to find the critical points. xyFFTo 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=xF0=yF0=F3) 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
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