The River City Police Department uses work shifts in which officers 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. A total of 6 officers must be on duty Monday, Tuesday, Wednesday, and Thursday;

10 are required on Friday and Saturday; and 8 are needed on Sunday. River City wants to meet these staffing needs with the minimum total number of officers.

(a) Formulate a shift scheduling LP to select an optimal staffing plan.

(b) Which of the constraints of your model are covering constraints? Explain.

(c) Enter and solve your model with the class optimization software.