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

[Metahominid]

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 \sum^{n}_{i=1}a_{i}x^_{i}subject to the constraint \sum^{n}_{i=1}x^{2}_{i} = 1

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.

 

[Tedjn]

Have you studied Lagrange multipliers?

 

[Metahominid]

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.

 

[darkside00]

How do you apply that to the above series though?