Maximizing sum of products from two finite sets

[sparsh12]

if {x₁ , x₂ , ...x_i} and {y₁,y₂,...y_i} are finite sets.

are two sets of real numbers. Then sum

Ʃ x_ix_j +y_iy_j must be maximum, and i≠j

so is there some general condition to solve this problem?

 

[Norwegian]

Is there anything in there, variables, summation rules, conditions, indexing, etc, that is allowed to vary? If so, you should tell us, and if not, your question is equivalent to asking for the maximum of the number x.

Perhaps you really don't mean to have that Ʃ there, in which case you get an actual question.

 

[sparsh12]

I have changed the question,under the title: Travelling Salesman Problem, in number theory page.