Optimisation Lagrangian Problem

It seems like Lagrange multiplier theory would be applicable here, specifically for the optimization problem of maximizing f(x, y) subject to the constraint g(x, y) = c. This is similar to the question you are struggling with, so it would be helpful to review the theory and see how it applies to your problem.
  • #1
JoshMaths
26
0
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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  • #2
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.
 
  • #3
Thanks
 

Related to Optimisation Lagrangian Problem

1. What is the Optimisation Lagrangian Problem?

The Optimisation Lagrangian Problem is a mathematical concept used to find the maximum or minimum value of a function subject to one or more constraints. It involves the use of Lagrange multipliers, which are variables used to incorporate the constraints into the function.

2. How is the Optimisation Lagrangian Problem solved?

The Optimisation Lagrangian Problem is solved using the method of Lagrange multipliers. This involves finding the critical points of the function using the partial derivatives and then solving the resulting system of equations to find the optimal solution.

3. What are the applications of the Optimisation Lagrangian Problem?

The Optimisation Lagrangian Problem has many applications in various fields such as economics, engineering, and physics. It is used to optimize resource allocation, minimize costs, and maximize efficiency in various systems and processes.

4. What are the advantages of using the Optimisation Lagrangian Problem?

The Optimisation Lagrangian Problem allows for the incorporation of constraints into the objective function, making it a more realistic and applicable approach to optimization problems. It also provides a systematic and efficient method for solving complex problems with multiple constraints.

5. Are there any limitations to the Optimisation Lagrangian Problem?

One limitation of the Optimisation Lagrangian Problem is that it requires the constraints to be differentiable, which may not always be the case in real-world problems. It also assumes that the objective function is continuous and differentiable, which may not be true for all functions.

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