1.[15 points] Recall the nurse-scheduling problem introduced in class. Suppose that in addition to fulltime nurses who work 5 days with two consecutive days off, part time nurses who work any 2 consecutive days (with 5 days off) are available. Full-time nurses are paid $100/ day; part-time nurses are paid $80/ day. A hospital policy is that there may not be more part-time nurses than full-time nurses on the roster. Find the minimum-cost staffing plan (i.e., the number of part-time and full-time nurses on each possible tour) so that the daily staffing needs are met. How did you reformulate the decision variables, objective function, and constraints? Show your mathematic formulation of this problem. You do not need to solve this