Problem 1 A hospital's ER needs to keep doctors on call, so that a qualified individual is available to perform every medical procedure that might be required (there is an official list of such procedures). For each of several doctors available for on-call duty, the additional salary they tend to be paid and which procedures they can perform, is known. The goal to choose doctors so that each procedure is covered, at a minimum "cost". For example, there are five procedures that the hospital needs doctors to be on call for, and there are six doctors that they can schedule to be on call (Table Table 1: Set of doctors and the procedure they are trained to perform Procedure 1 Doctor 1 Doctor 2 Doctor 3 Doctor & Doctor 5 Doctor 6 Procedure 2 Procedure 3 Procedure 4 Procedure 5 (a) Model the problem as an IP such that the hospital schodes the least sumber of doctors on call and cor each procedure (b) Now assume that the cost for each doctor is different, Doctor 1: $200, Doctor 2 $140, Doctor 3: $10 Doctor 4 $150, Doctor such that the cost is minimized. 130 Doctor & $220 Change the objective ti tive days, such that they cover all (e) The hospital wants to schedule doctors for two procedures in each day and a doctor is not on call two days a (d) Adding to the model in part (a), the hospital realized they cannot schedule doctor 1 and doctor 4 onto the same shift. How would that change the model? (e) Adding to the model in part (a), the hospital decided that if they schedule doctor 5 then they must also schedule doctor 6, and vice versa. They can also schedule neither. (f) Adding to the model in part (a), the hospital realized that there has been a higher coverage need for procedure 1, and they would like to have at least two on call doctors that can perform it.