Bipartite Graphs and Matchings · Hard problem

A compatibility graph has workers $1,2,3,4,5,6$ and machines $a,b,c,d,e,f$: workers $1,2,3$ are each compatible only with machine $a$; workers $4,5$ are each compatible with machine $b$ or machine $c$; worker $6$ is compatible with machine $d$, $e$, or $f$. What is the minimum number of workers-or-machines needed to touch every listed compatibility in this $12$-vertex network?