3. The weekly cafeteria cooking staff schedules need to be established. All cooks work 12-hour shifts, 4 days in a row. Then they take 3 consecutive days off. There are seven possible schedules (Monday, Tuesday, Wednesday off; Tuesday, Wednesday, Thursday off; etc.) The following table lists the number of cooks needed each day of the week as well as their pay.

Formulate and solve an integer linear programming model that will determine the number of cooks in each schedule while minimizing weekly costs and ensuring that minimum capacity needs are met.