Directed Graphs and Network Flows · Superchallenge problem

A distribution system has two depots $s_1,s_2$ and two stores $t_1,t_2$, linked through warehouses $a,b$ with capacities $c(s_1,a)=4$, $c(s_1,b)=3$, $c(s_2,a)=2$, $c(s_2,b)=5$, $c(a,t_1)=3$, $c(a,t_2)=2$, $c(b,t_1)=3$, $c(b,t_2)=2$. Warehouse $b$ can additionally handle at most $4$ units in total (regardless of how its individual links are used), while $a$ has no such extra limit. What is the maximum total amount that can reach the two stores combined?