Assume you are given a bipartite graph $G = (U, V, E)$ and you are given an integer $n$. Assume also that for each $v \in V$, you are given two integers $v_{min}$ and $v_{max}$ (where $v_{min} \le v_{max}$).
The problem is to find a subset $U'$ of $U$ of size $n$ such that for each $v \in V$, the number of edges coming into $v$ from $U'$ is between $v_{min}$ and $v_{max}$.
Given a problem like this, can we determine efficiently whether there is a solution? And, if there is a solution, can we find one efficiently?
If we can't do so efficiently, is there an approximation algorithm?