What is the maximum of a series with positive numbers and a constraint?

  • Thread starter Metahominid
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In summary, the conversation discusses finding the maximum value of a series with a constraint, using Lagrange multipliers. The topic was brought up due to a problem on a multivariate calculus final exam. The speaker initially struggled with formulating the problem in terms of functions, but eventually remembered the concept of constraints and how to apply it to the given series.
  • #1
Metahominid
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So I ran into this on my multivariate calculus final this morning, I don't think anyone did it but it has been stuck in my head and I have run out of thoughts.

Let a1, a2, …, an be n positive numbers.
Find the maximum of [tex]\sum^{n}_{i=1}a_{i}x^_{i}[/tex]subject to the constraint [tex]\sum^{n}_{i=1}x^{2}_{i} = 1[/tex]

Alright I've never used Latex but I believe that worked. Not quite sure, where to go looks like power sums of power 1,2.
 
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  • #3
Yes, we studied it. About an hour ago I saw the word constraint and it popped into my head but I got discouraged when I tried to formulate it in the terms of functions. I wasn't entirely sure I could say that the summations were functions. I figure I need walk around for a moment and I will see it.
 
  • #4
How do you apply that to the above series though?
 

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