Help needed in AEHASH

Hi, I was trying to understand AEHASH

but I was not able to understand from this line -> DP(V, A, E) = sum { DP(V1, A1, E1) * DP(V2, A2, E2) }

Why do we multiply here DP values ? and what does -> max(V1, V2) = V - A signify ?

Can anyone who solved it or understood the concept of solving explain it ??