Please show all work and explain the constraints and objective function. Please do this by hand and not through excel or any other program for a like. Thank you!

Question 2: The head nurse of Lakuen Health System (LHS) lab center needs to make decision on how to schedule its nurses for the following week. The head nurse has a prediction to determine how many nurses will be required to cover the demand. At least d nurses must be scheduled on day i to ensure patients receive adequate care. Also due to the hospital regulations, there are limits to how many shifts each nurse can work. Nurse n must work at least shifts, but cannot work more than my shifts. To accommodate nurses' scheduled vacation, the head nurse constructs an availability table for all nurses where in the table ani = 1 if nurse n is available on day i; ani = 0 otherwise. Nurses cannot work on days that they are not available. Each nurse n is paid Pn per shift work. a. Develop an optimization model to help LHS lab head nurse to minimize the labor cost of next week; clearly define any notation that you use. b. What type of an optimization problem is this? (LP, IP, MIP, etc.). Clearly explain your answer. n Question 2: The head nurse of Lakuen Health System (LHS) lab center needs to make decision on how to schedule its nurses for the following week. The head nurse has a prediction to determine how many nurses will be required to cover the demand. At least d nurses must be scheduled on day i to ensure patients receive adequate care. Also due to the hospital regulations, there are limits to how many shifts each nurse can work. Nurse n must work at least shifts, but cannot work more than my shifts. To accommodate nurses' scheduled vacation, the head nurse constructs an availability table for all nurses where in the table ani = 1 if nurse n is available on day i; ani = 0 otherwise. Nurses cannot work on days that they are not available. Each nurse n is paid Pn per shift work. a. Develop an optimization model to help LHS lab head nurse to minimize the labor cost of next week; clearly define any notation that you use. b. What type of an optimization problem is this? (LP, IP, MIP, etc.). Clearly explain your answer. n