Bipartite Graphs and Matchings · Hard problem

A network splits into two separate pieces. In the first piece, workers $p_1,p_2,p_3$ can each be assigned only to task $x$ or task $y$. In the second piece, stations $q_1,r_1,q_2,r_2$ are wired in a $4$-cycle $q_1\text{-}r_1\text{-}q_2\text{-}r_2\text{-}q_1$, and a "cover" there means a set of stations touching every wire. What is the minimum total number of tasks, workers, and/or stations needed so that every worker-task pairing in the first piece AND every wire in the second piece is touched by the chosen set?