Determine the 5 vertices of the feasible region, given the constraints below.
to help. (Make sure to include a sketch or screenshot of your graph when you upload your work.) 3x+5y≤30 x≤9 y≤3 x≥0 y≥0 (1 point) Responses (3,6) (3,6) (9,3) (9,3) (9,0) (9,0) (0,3) (0,3) (5,3) (5,3) (0,5) (0,5) (9,3) (9,3) (9,2) (9,2) (0,0) (0,0) (9,0.6)
The 5 vertices of the feasible region are:
(9, 0)
(0, 3)
(0, 0)
(9, 3)
(3, 6)
Please refer to the sketch or screenshot of the graph for a visual representation of the feasible region.
To determine the vertices of the feasible region, we need to plot the given constraints on a graph:
1. The first constraint is 3x + 5y ≤ 30. To plot this line, we need to find two points that satisfy the equation when it is converted into the y-intercept form (y = mx + b). Suppose x = 0, then we have 5y ≤ 30, so y ≤ 6. This gives us the point (0, 6). Suppose y = 0, then we have 3x ≤ 30, so x ≤ 10. This gives us the point (10, 0). Plotting these two points and drawing the line between them, we have a line segment.
2. The second constraint is x ≤ 9. This is a vertical line passing through x = 9.
3. The third constraint is y ≤ 3. This is a horizontal line passing through y = 3.
Now, we need to find points of intersection for the lines:
- The first constraint intersects the second constraint at (9, 3).
- The first constraint intersects the third constraint at (5, 3).
Finally, we need to determine the points of intersection for the horizontal and vertical lines:
- The second constraint intersects the third constraint at (9, 3).
Therefore, the vertices of the feasible region are: (0, 0), (0, 3), (5, 3), (9, 3), and (9, 0).
To determine the vertices of the feasible region, we need to first graph the constraints and then identify the points where the lines intersect. Since the given constraints are inequalities, the feasible region will consist of the area that satisfies all the constraints.
The given constraints are:
1) 3x + 5y ≤ 30
2) x ≤ 9
3) y ≤ 3
4) x ≥ 0
5) y ≥ 0
To graph these constraints, we will start by plotting the equations of the lines that represent each constraint.
1) 3x + 5y ≤ 30:
To plot this line, we can rewrite the inequality as an equation and then graph it.
3x + 5y = 30
Solving for y, we get:
y = (30 - 3x)/5
We can now plot this line on the graph.
2) x ≤ 9:
This is a simple vertical line passing through x = 9.
3) y ≤ 3:
This is a simple horizontal line passing through y = 3.
4) x ≥ 0:
This is the y-axis of the graph.
5) y ≥ 0:
This is the x-axis of the graph.
After plotting all the lines, shaded the area that satisfies all the constraints. The area bounded by the lines and shaded in the graph represents the feasible region.
To determine the vertices of the feasible region, we need to identify the points where the lines intersect. These points will be the vertices.
From the given response options, it appears that the vertices of the feasible region are:
(3, 6), (9, 3), (9, 0), (0, 3), and (0, 0).
Please note that without a visual representation or an actual graph, it is challenging to confirm the accuracy of the provided vertices. It is recommended to double-check these points on the actual graph or provide a sketch or screenshot of the graph for further confirmation.