I have been reading optimization problems in communication area where it is a common practice to maximize rate of users as below objective function:
$\hspace{28mm} \text{ Maximize } \sum_k w_k \log r_k$
here, $r_k$ is the rate of an user, $w_k$ is the weight factor for every user. Weight factor may be decided on any specific criteria such as: users availability, distance from base station etc. Now I do understand that taking log makes it a convex optimization and ensures fair proportion among users but I cant understand how the weight factor is helping to maximize the rate individual users.
So my question is, why weight factor is used in the above equation and how it is helping each user to achieve a higher rate.