Personnel Assignment

There are six Marines eligible for re-assignment, and seven assignments are available. The military has developed a composite measure of preference for each Marine and assignment, based on the desires of the individuals and the service. Shown below are the soldier-assignment combination preferences, and a blank space indicates that the Marine is not eligible for that match.

The following restrictions also apply to the matching, which may or may not assign all of the Marines:

1. At least one of Marines 1 and 2 must be given an assignment.
2. At most two of Marines 4, 5, and 6 may be given an assignment.
3. At least two of the assignments 1, 2, and 3 must be filled.
4. At least one but no more than three of assignments 4 through 7 must be filled.  
5. At least four assignments must be filled.

Assignment:

1. Design a pure network model to identify a matching of Marines to assignments that maximizes the overall preference, subject to the constraints above.
2. How would you change the model to add a first priority goal of maximizing the number of assignments, with a secondary goal of maximizing the overall preference?
3. How would your model change if restriction 4 could be violated (in either direction) with a preference penalty of 10?