Calc III Ch13 Notes_Part30

Calc III Ch13 Notes_Part30 - 13.10 —— Lagrange...

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Unformatted text preview: 13.10 —— Lagrange Multipliers In “real life” most optimization problems have restrictions. Why? If you’ve ever done Linear Programming, you’ve seen this before. Why is this so limited? Here we can solve optimization problems with constraints whose functions are of a variety of forms. Think of the objective function (which we’re trying to optimize) as a family of . The optimal solution is going to occur when a level surface is “ ” the constraint. How will these two surfaces be touching? What do we know about the surfaces at this point? What do we know about parallel vectors? Method of Lagrange Multipliers: Let f(x, y) be the objective function and g(x, y) be the constraint. 1. From the equation , use the corresponding terms to set up a system of equations along with the constraint to solve for all variables. 2. Evaluate the optimal solutions to determine max/mins. ...
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