1. Write out a full mathematical formulation of an optimization problem that solves Meg's scheduling problem. Clearly explain all decision variables and constraints.

2. Solve the optimization problem and provide a managerial discussion of the results.

3. What if Meg gives you a rank-ordering of the relative importance of the different soft constraints? How can you update your model formulation to handle this?

4. Meg indicated that a hard constraint was to avoid scheduling pediatricians for shifts they requested off. What if there is no feasible solution for a given set of vacation requests? While this has not posed a problem for their practice yet, discuss ways the optimization tool might help Meg deal with this situation should it arise in the future.

5. Discuss some options for putting the scheduling tool in Meg's hands. This question moves beyond the math of the problem and is intended to have you think about user experience, user interface, and, more generally, how to move your work into production. What questions might you ask Meg to provide some recommendations on this