A hospital requires different numbers of full-time nurses on different days of the week. The minimum number of full-time nurses required each day is given below. Each nurse works for 5 consecutive days, followed by 2 days off repeated each week. Nurses are paid $200 per day on weekdays and $300 per day on weekends. Day of the week Min. required nurses 17 Monday Tuesday 13 Wednesday 10 Thursday 12 Friday 14 Saturday Sunday 25 20 a) Formulate a linear program (math problem) to minimize the total cost of meeting the nurse requirements for the hospital. c) Solve the LP for how many nurses to hire for each day. What are the optimal number of nurses starting each day and what is the total cost for the week? 4. Part 2 extra credit: b) (5pts extra credit) Suppose the hospital can hire both full-time and part-time nurses. Part-time nurses can be hired on a daily basis and there is no restriction on their schedule. Each part-time nurse is paid $250 per day. Modify the formulation of the linear program in part A to include both full-time and part-time nurses. d) (5pts extra credit) Solve the LP for how many nurses of each kind to hire for each day.