I'm just gonna go ahead and write budget or B for budget here so you're trying to maximize revenues, and then you have some You'd have would be, let's say a budget so You're kind of modeling your revenues based on different choices you could make running that company, and the constraint that Practice is if this was, say a revenue functionįor some kind of company. To this contour of g, and you know, a pretty classic example for what these sorts of things could mean, or how it's used in That we found was that you look through the variousĭifferent contour lines of f, and the maximum will beĪchieved when that contour line is just perfectly parallel The last couple of videos, and kind of the cool thing You are limited to the values of x and y that satisfy this property, and I talked about this in So we say you can't look at any x, y to maximize this function. In this case, x squared plus y squared, and we want to say that this has to equal some specific amount. The reason we call it aĬonstrained optimization problem is 'cause there's some kind of constraint, some kind of other function, g of x, y. The goal is to maximize this guy, and of course, it's not just that. Look a little bit different, it's kinda nice that it has similar shapes so that's the function, and Outputs that constant, and if I choose a different constant, and that contour line can Happens if we set this equal to some constant, and we askĪbout all values of x and y such that this holds, such that this function I have pictured here is, let's see, it's x squared times e to the y times y so what I have shown here is a contour line for this function.
Optimization problem setup so we'll have some kind
So to remind you of the setup, this is gonna be a constrained Now we talked about Lagrange multipliers. Today I'm gonna be talking about the Lagrangian.
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