The constraints are set up based on the overlapping shifts. For example, the staff who start at 3 AM (X1) and 11 PM (X6) will cover the 3 AM to 7 AM period. Therefore, X1 X6 must be at least 3 to meet the minimum staff requirement for that period. Similarly, the staff who start at 3 AM (X1) and 7 AM (X2) will cover the 7 AM to 11 AM period. Therefore, X1 X2 must be at least 12. This pattern continues for all the periods. The last constraint, X1, X2, X3, X4, X5, X6 0, ensures that the number of staff cannot be negative. To solve this problem, you would use a linear programming method, such as the simplex method, to find the values of X1, X2, X3, X4, X5, and X6 that