Problem $1.$ Unate Covering: $(20$ points$)$

Solve the following covering problem.

NOTE: If Branch and Bound is needed at any point, use the following rules: $($i$)$ The next pivoting column should be selected as the one that covers the most rows. $($ii$)$ If there are no two independent rows in the cyclic core, the lower bound should be assumed to be equal to $2.$ Clearly identify the initial Upper and Lower Bounds and the partial solutions costs and any updates made to the best solution found in your steps.