Prove that "Finishing the degree in three years" problem is NP-Complete
Consider an instance $(G,k)$ of the clique problem: deciding whether there is a clique of size $k$ in the graph $G$. Construct a course for each vertex (say "vertex course") and for each edge (say "edge course") in $G$. Each edge course has two precondition vertex courses corresponding to its two endpoints. In addition, we set $m_1=k,m_2=+\infty, m_3=m-\binom{k}{2}$ where $m$ is the number of edges in $G$. Now we can see there is a clique of size $k$ in $G$ if and only if it is possible to finish the degree in three years.