We already know the adjacency matrix of a directed network as follows. If we need to construct an entertainment center at one of the vertices, and require the longest distance from this vertex to...

We already know the adjacency matrix of a directed network as follows. If we need to construct an entertainment center at one of the vertices, and require the longest distance from this vertex to other vertices to be the shortest, and the total distance to be as short as possible. Where should the entertainment center be located? Write out the solving process.