HW2.6 (Integer Linear Program): Formulate the following nurse-staffing problems as integer linear programs, i.e., linear programs with further integer constraints on the decision variables. Solve them using the Excel Solver. For a typical day, a hospital administrator has the following minimal daily requirements for nursing personnel: Period Clock Time (24-hour Day) Minimal # of Nurses Required 1 6 AM -- 10 AM 60 10 AM - 2 PM 70 3 2 PM - 6 PM 60 6 PM -- 10 PM 50 5 10 PM - 2 AM 20 6 2 AM - 6 AM 30 2 4 Part (a): Assume that the hospital hires only full-time nurses, and the nurses begin service at the start of a period and work for 8 consecutive hours. The hospital wants to determine a work schedule for the typical day that requires the least number of nurses while satisfying the requirements. Formulate this problem as an integer linear program. First, ignore the integer requirements. Then, impose the integer requirements and compare the difference. Part (b): Now assume that the hospital also hires temporary nurses who work four-hour shifts, i.e., part-time, and begin service at the start of a period. Also assume that a full-time nurse costs $20 per hour while a temporary (part-time) nurse costs 514 per hour, and that the cost does not vary with shift. Formulate an integer linear program to determine how the hospital can minimize the total cost of nurse staffing for the typical day while satisfying the requirements. First, ignore the integer requirements. Then, impose the integer requirements and compare the difference. Part (c): Finally, since temporary (part-time) nurses are hired through an agent that may send different nurses to the hospital on different days, the full-time nurses need to supervise the temporary (part-time) nurses. Assume that such supervision takes full-time staff's time away from their actual nursing duties. Also assume that each temporary (part-time) nurse would require supervision time that is equivalent to 0.25 of a full-time nurse's. Modify the linear program formulated for Part b to formulate an integer linear program for this new problem. Note that there must be sufficient full-time staff to supervise the part-time staff for each time period. First, ignore the integer requirements. Then, impose the integer requirements and compare the difference