Nurses in the Pediatrics Unit at Mott Hospital work shifts in which nurses work 5 of the 7 days of the week with 2 successive days off. For example, a shift might work Sunday through Thursday and then have Friday and Saturday off. Based on historical data, it is known that a at least 5 nurses are needed on duty Monday, Tuesday, Wednesday, and Thursday; 7 are required for Friday and Saturday; and 6 are needed on Sunday. There are a total of 9 nurses that can be scheduled.
a) Formulate a linear program that maximizes the number of weekend days off received by the nurses (weekend is Saturday and Sunday). Clearly define your decision variables, explain your formulation of the objective function, and describe what each of your constraints means in words.