Please solve within 2 hours

Problem 2 (18 points) A virus pandemic is approaching the nation, and hospitals understand the need for a larger staff. Their plan is to hire more nurses, where hired nurses will be either night or day shift nurses. Each nurse will work three shifts (three nights or three days), have a day off, work two shifts (two nights or two days), and then have a day off each week. The nurses weekly schedule is set from hiring, and it stays that way for their hiring period. The hospital needs to accommodate the projected demand for nurses and satisfying the minimum requirement they had set (specified in the table below). To maintain a certain doctor to nurse ratio, the hospital does not want to hire more than 30 nurses total. They would like to also hire at most 17 day shift nurses and at most 13 night shift nurses. Day of week Night Shift Day Shift Saturday Sunday Monday Tuesday Wednesday Thursday Friday (a) Model the problem as a linear program such that the hospital minimizes the total number of new nurses hired. (9 points) (b) The model in part (a) can be separated into two disjoint models - how? Write down one of them. (4 points) (c) Health officials estimate that the pandemic will be a year long. The hospital would only like to hire the nurses for that year. It costs the hospital $130 and $100 per nurse per night and day shift, respectively. The hospital also allocated a total budget for this year at a million dollars. If the hospital wants to minimize that year's cost (assuming 52 weeks/year), how would that change the model in part (a)? Change it. (5 points) Problem 2 (18 points) A virus pandemic is approaching the nation, and hospitals understand the need for a larger staff. Their plan is to hire more nurses, where hired nurses will be either night or day shift nurses. Each nurse will work three shifts (three nights or three days), have a day off, work two shifts (two nights or two days), and then have a day off each week. The nurses weekly schedule is set from hiring, and it stays that way for their hiring period. The hospital needs to accommodate the projected demand for nurses and satisfying the minimum requirement they had set (specified in the table below). To maintain a certain doctor to nurse ratio, the hospital does not want to hire more than 30 nurses total. They would like to also hire at most 17 day shift nurses and at most 13 night shift nurses. Day of week Night Shift Day Shift Saturday Sunday Monday Tuesday Wednesday Thursday Friday (a) Model the problem as a linear program such that the hospital minimizes the total number of new nurses hired. (9 points) (b) The model in part (a) can be separated into two disjoint models - how? Write down one of them. (4 points) (c) Health officials estimate that the pandemic will be a year long. The hospital would only like to hire the nurses for that year. It costs the hospital $130 and $100 per nurse per night and day shift, respectively. The hospital also allocated a total budget for this year at a million dollars. If the hospital wants to minimize that year's cost (assuming 52 weeks/year), how would that change the model in part (a)? Change it. (5 points)