Partitioning a matrix into equal-sized regions: finding the maximum
In the proof of theorem 2 in Improved Approximation Algorithms for Rectangle Tiling and Packing by Berman et al, they proved an upper bound of $\frac{11}{5} \max\{W/p,y\}$, where $W$ is the sum of the weight of all elements, $p$ is the number of rectangles and $y$ is the weight of the largest element. 

This implies a upper bound of $\frac{11}{5j}$ for your problem.