# Partitioning problem

This is the combination of packing and covering. Its IP form is $LaTeX: \textstyle \mbox{Opt}\left \{cx: Ax=b, x \in \left \{0,1 \right \}^n \right \},$ where Opt could be Min or Max, and $LaTeX: A$ is a 0-1 matrix. The equation $LaTeX: \textstyle A(i,.) x = b_i$ means that exactly $LaTeX: b_i$ elements must be selected from set $LaTeX: i.$ In particular, a multiple choice constraint is $LaTeX: \textstyle \sum_j x_j = 1.$