For a matrix $c (m\times n)$ of non-negative constants, find values of $\lambda_1, \lambda_2, \ldots, \lambda_n$ that satisfy $\sum_{k=1}^n \lambda_k = 1$, $\lambda_k \ge 0 \, \forall k$ and maximize

\begin{equation*} L = \sum_{i=1}^m \log \sum_{k=1}^n \lambda_k c_{i,k} \end{equation*}