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From: Luis Felipe on 28 May 2010 17:57
Thank you, christian.bau and Rob Johnson. They are very interesting
ways to solve this problem. I had used the lagrange multipliers to
solve that. However, my problem is to know if that optimization
problem has been used in any application (for example, biology or
engineering). I want to interpret the p_i and the a_i (and the
optimization function), and to know what the solution could mean into
this interpretation.
Thank you for your comments.

Luis Felipe
From: Luis Felipe on 28 May 2010 17:59
And thank you, Tony.
From: Tony on 28 May 2010 18:01
On May 28, 11:59 pm, Luis Felipe <luispip...(a)gmail.com> wrote:
> And thank you, Tony.

You mean, "I'm sorry I wasted all your time", don't you?
From: Luis Felipe on 28 May 2010 18:01
On May 28, 4:59 pm, Luis Felipe <luispip...(a)gmail.com> wrote:
> And thank you, Tony.

Sorry!
From: Ray Vickson on 29 May 2010 02:45
On May 28, 2:11 pm, Luis Felipe <luispip...(a)gmail.com> wrote:
> Hi,
>
> Have you ever seen the following optimization problem?:

It is the type of problem Economists look at, where the p_i are
factors of production, the objective prod(p_i)^a_i is a so-called Cobb-
Douglas production function, and the constraint is a limitation on
total availability. See http://en.wikipedia.org/wiki/Cobb%E2%80%93Douglas
for references and solution details.

R.G. Vickson

>
>              n
> max   prod (p_i)^a_i
>            i=1
>
>                                   n
> subject to                sum  p_i  =  1
>                                  i=1
>
> where   a_i   is a positive constant for i=1,...,n
>
> I would like to know if that optimization problem has any application
> (or has been used to solve anything). Thank you for your comments.

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