1. A local hospital has been experiencing labor shortages and needs to find ways to improve efficiency. One source of inefficiency that has been identified is operating room scheduling. There are four surgeons scheduled to work tomorrow. In the table below you can find tomorrow's scheduled patients and the estimated time their surgery case will require. Note that each patient should be operated on by only one surgeon, that all of the surgeons are capable of performing all types of surgery for the day, and that all patients only need one surgery. The surgery teams start their cases at 7am and are all contractually obligated to receive overtime pay (time and a half) if they are working past 5pm. Find the optimal surgery schedule which allows all patients to be treated while minimizing the amount of time that each surgeon deviates from the standard workday. a. Formulate a mathematical programming model using binary variables for this problem in Excel. b. Report the schedule by explaining which patients each surgeon will operate on. C. Will the optimal schedule require paying any over time? d. Will the optimal schedule allow any surgeons to leave early for the day? Operating Room Allocation Patient 1 Estimated Hours Required 3.0 2 6.0 3 4.0 4 3.0 5 1.0 6 4.5 7 5.0 8 2.0 9 2.0 10 4.0 11 3.0 12 1.5