I need some algebra help to come up with a solution to the maximum entropy formulation of the gravity model. The problem: $ \hspace{35pt}\\ max \ H =-\sum_{i=1}^I \sum_{j=1}^J T{_i}_j\ln( T{_i}_j) \\ \sum_{j=1}^J O_i \hspace{35pt} i =1,..,I \\ \sum_{i=1}^I D_j \hspace{35pt} j =1,..,J \\ \sum_{i=1}^I \sum_{j=1}^J c{_i}_jT{_i}_j \le \bar C \\ T{_i}_j \ge 0, \hspace{35pt} i=1,..,I, \hspace{10pt} j =1,..,J $
And to show that the solution to the problem equals :$\ T{_i}_j = r_is_i{\rm e}^{-\lambda c{_i}_j }$ . I think that i should make use of a Lagrange-multiplier so get the lambda, but I do not know how. Can somebody help me here, or give some links to solutions?
/U