(A scheduling model, 18 points in total) Prisma Health needs your help with scheduling nurses in their intensive care unit (ICU) for COVID-19 patients. For this exercise, we will assume the same schedule is repeated every day and the requirements for nurses are the same every day. Nurses work can work either 8 or 12 hour shifts, and can start their shift at the following times: 12AM, 4AM, BAM, 12PM, 4PM, 8PM. Shifts that start in the evening also cover the time in the morning. For example, a 12-hour shift starting at 8PM covers the times 8PM until 8AM of the next morning.) The table below indicates the number of nurses that are required during all the 4-hour time windows of a day. The salary of each nurse on an 8-hour shift is $100 per shift, and the salary of each nurse on a 12-hour shift is $180 per shift. Period Number of nurses required 12am -- 4am 8 4am -- 8am 6 15 8am -- 12pm 12pm -- 4pm 12 4pm -- 8pm 10 8pm -- 12 am 7 Formulate a linear program that can help Prisma Hospital determine how to schedule the nurses to meet the requirements throughout the day and minimize the total cost. Be sure to clearly define all decision variables and explain the objective and constraints of your model