Question

The constraints of a problem are listed below. What are the vertices of the feasible region?

2x + 3y < 6
2x - 2y ≥ -3
x > 0
y ≥ 0

Option 1: (0, 0), (0, 0.5), (0, 2), (3, 0)
Option 2: (0, 0), (0, 2), (1.5, 1), (3, 0)
Option 3: (0, 0), (0, 0.5), (1.5, 1), (3, 0)
Option 4: (0, 0), (0, 0.5), (1, 1.5), (3, 0)

Answer 1

To find the vertices of the feasible region, we need to graph the system of inequalities and identify the points where the boundaries intersect. The correct vertices of the feasible region are (0, 0), (0, 0.5), (1.5, 1), (3, 0).

Step-by-step explanation:

To find the vertices of the feasible region, we need to graph the system of inequalities and identify the points where the boundaries intersect. Let's start by graphing the first inequality, 2x + 3y < 6. We can rewrite this inequality as y < (-2/3)x + 2 using slope-intercept form. Next, let's graph the second inequality, 2x - 2y ≥ -3. We can rewrite this inequality as y ≤ x + 3/2. Now, let's plot these two lines and shade the region that satisfies both inequalities. The feasible region is the overlapping shaded area. Finally, we can identify the vertices of the feasible region, which are the intersection points of the boundary lines. The correct option with the vertices is Option 3: (0, 0), (0, 0.5), (1.5, 1), (3, 0).