Optimisation Lagrangian Problem

[JoshMaths]

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

 

[CompuChip]

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.

 

[JoshMaths]

Thanks