Hex-agony #2 I: One Black at the Centre

The board is a small hexagon of 19 hexes, arranged in 5 columns of 3, 4, 5, 4 and 3 hexes.
One number is already given: a blue 11 in the top hex of the fourth column (marked B11 below).

Write non-negative integers, each coloured red, blue, green or black, in some (perhaps not all) of the other hexes so that every number on the board, including the given 11, obeys its colour's rule:

1. Each red number equals the sum of the blue numbers in its view.
2. Each blue number equals the maximum of the green numbers in its view (or 0 if it sees no green).
3. Each green number equals the product of the black numbers in its view (or 1 if it sees no black).
4. Each black number equals the number of red numbers in its view.

A hex's view is every other hex in the same column or on either of the two diagonals through it (a diagonal steps one column left or right and half a hex up or down at each step, as in the diagram, and runs all the way to the edge of the board).
Nothing blocks the view, and empty hexes count for nothing.

Answer format: a single integer, the largest possible sum of all the numbers in the middle column (the column of 5 hexes); empty hexes count as 0.