<s>[INST] Consider the set of customers $C=\{c_1,c_2,c_3,c_4\}$ and four service providers $\{S_1,S_2,S_3,S_4\}$. Any provider $S_i$ can serve at most $K$ customers, where $K$ is a fixed constant.  Define a customer $c_i$ is served iff there is an edge from $c_i$ to some provider $S_j$. Also,  each edge $\{c_i,S_j\}$ is labeled with a value $w$ (e.g. $w_{i,j}$),  which means the cost of provider $S_j$ serving customer $c_i$.
The goal is to find a subgraph with $4$ edges that represents  assign customers to providers such that $\sum w_{i,j} $ is minimized.
Here we have $K=2$ and the following costs:
\begin{array}{c|c c c c}
 & S_1 & S_2 & S_3 & S_4\\
\hline
c_1 & 15 & 20 & 25 & 30\\
c_2 &  35 & 40 &  10 & 15\\
c_3 & 25 & 15 & 30 & 20\\
c_4 & 40 & 25 & 15 &  5
\end{array}
Does it possible to find the subgraph which contains only the edges with weight at most 20, and assignment for each of $c_1,c_2,c_3,c_4$ can be finished within 120?[/INST]