Optimisation Lagrangian Problem

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    Lagrangian Optimisation
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SUMMARY

The discussion centers on the application of Lagrangian optimization techniques to solve a two-variable optimization problem involving constraints. The participants emphasize the importance of understanding Lagrange multipliers, particularly in maximizing a function subject to a constraint. The specific variables mentioned, such as px and qy, represent constants multiplied by the respective variables, which are crucial for formulating the optimization problem correctly. The conversation highlights the necessity of grasping the foundational concepts of Lagrangian methods to effectively tackle such problems.

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  • Understanding of Lagrange multipliers
  • Familiarity with two-variable optimization techniques
  • Basic knowledge of constraint functions
  • Ability to interpret mathematical expressions and constants in optimization
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  • Study the theory of Lagrange multipliers in detail
  • Practice solving two-variable optimization problems
  • Explore constraint optimization examples in calculus
  • Review mathematical functions and their graphical representations
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Students, mathematicians, and professionals in fields requiring optimization techniques, particularly those dealing with constrained optimization problems.

JoshMaths
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No this is not homework.

http://imgur.com/zAZxmuC
http://imgur.com/zAZxmuC

Ok i am struggling to even start this question.

I see it has a constraint so i would be tempted to use Lagrangian but from there i don't see how px and qy fit into it?

Some assistance on the tools needed to approach this question would be great, it may be two-variable optimisation but i don't really have a handle on that either.

Thanks,

Josh
 
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It looks like Lagrange multiplier theory would come in handy. Look at the intro to this Wikipedia page...

For instance (see Figure 1), consider the optimization problem
maximize ##f(x, y)##
subject to ##g(x, y) = c##
That is exactly your problem (for suitable f, g and c).

Note that px is just one of the given constants p multiplied by the variable x, I'm not sure why that confuses you.
 
Thanks
 

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