Question

Which of the points is not one of the vertices (s, t) of the shaded region of the set of inequalities shown below?

ss30 - 3t
s2 15-1
S25-1
s20
120
A. (7.5, 7.5)
B. (15,0)
C. (7.5, 0)
D. (22.5, 2.5)

Answer 1

The point (22.5, 2.5) is not one of the vertices of the shaded region of the set of inequalities.

Step-by-step explanation:

The points (s,t) that lie within the shaded region of the given set of inequalities can be determined by solving each inequality separately and then finding the common region where all the solutions overlap. Let's analyze each inequality:

1. s≥30 - 3t, which represents a line passing through (30, 0) and (0, 10). The points on or above this line are in the shaded region.
2. s≤2 + 15t-1, which represents a line passing through (2, 0) and (0, 3). The points on or below this line are in the shaded region.
3. s≥25-1, which represents a vertical line passing through (24, 0). The points to the right or on this line are in the shaded region.
4. s≤20 + 120/t, which represents a curve that starts at (0, 6) and approaches the vertical axis. The points below or on this curve are in the shaded region.

By analyzing the inequalities, we can determine that the point (22.5, 2.5) is not one of the vertices of the shaded region because it lies above the curve represented by the fourth inequality. Therefore, the correct answer is D. (22.5, 2.5).