Final answer:
After testing each point against the set of inequalities, it's found that Point B: (7.5,0) does not satisfy all of them and thus is not a vertex of the shaded region.
Step-by-step explanation:
The question is asking us to determine which of the given points is not a vertex of the shaded region defined by a set of inequalities. Given the inequalities and points, we can test each point against the inequalities to see if it satisfies them all. The inequalities are:
- s ≤ 30 - 3t
- s ≥ 15 - t
- s ≤ 25 - t
- s ≥ 20
Now, let's plug each of the points (s, t) into the inequalities to check which one does not satisfy all of them:
- Point A: (15,0) satisfies all inequalities.
- Point B: (7.5,0) does not satisfy the inequality s ≥ 20, making it the point that is not a vertex of the shaded region.
- Point C: (22.5, 2.5) satisfies all inequalities.
- Point D: (7.5, 7.5) satisfies all inequalities.
Therefore, the answer is Point B: (7.5, 0).