One aspect of the problem that has been ignored to this point is that each approved project must be led by a senior project manager. Julie has identified only eight senior managers who qualify and are available, and each of these can manage at most one project. In addition, some of these managers are not qualified to manage some projects. This information is summarized in the table below, where $1$ indicates that the manager is qualified for the project and $0$ indicates otherwise. The company$$s problem is the same as before, but now extra decisions have to be made: which manager should be assigned to each approved project? Of course, a project can$$t be approved unless a qualified manager is assigned to it$.$

Manager $1$ Manager $2$ Manager $3$ Manager $4$ Manager $5$ Manager $6$ Manager $7$ Manager $8$

Project $111111000$

Project $211110101$

Project $310011101$

Project $401001111$

Project $511111110$

Project $611111111$

Project $711111101$

Project $811110110$

Project $911110001$

Project $1011110111$

Project $1111111101$

Project $1200011011$

Optimal Solution

Determine which manager should be assigned to each approved project.

Enter a manager number for each approved project in the questions below. If a project is not approved, write "none."