Objective function: C=5x−4y Question 1 Using a graphing calculator, find and select all the vertices for the feasible region.(1 point) Responses (0,3) (0,3) (1,0) (1,0) (-3,0) (-3,0) (3,0) (3,0) (1.5,1.5) (1.5,1.5) (0,1) (0,1) (0,0)
The vertices for the feasible region can be determined by finding the intersection points of the lines that form the constraints. Since the constraints are not given in the question, the vertices cannot be determined.
To find the vertices of the feasible region, we need to solve the system of inequalities that determine it. Since the feasible region is not given, we cannot determine the exact vertices. However, based on the options provided, we can check which ones satisfy all the inequalities.
The standard form of the inequalities is:
x ≥ 0
y ≥ 0
5x - 4y ≤ C
Let's check each option:
(0, 3):
x = 0 and y = 3
Since 5(0) - 4(3) = -12, it does not satisfy 5x - 4y ≤ C.
(1, 0):
x = 1 and y = 0
Since 5(1) - 4(0) = 5, it does satisfy 5x - 4y ≤ C.
(-3, 0):
x = -3 and y = 0
Since 5(-3) - 4(0) = -15, it does not satisfy 5x - 4y ≤ C.
(3, 0):
x = 3 and y = 0
Since 5(3) - 4(0) = 15, it does satisfy 5x - 4y ≤ C.
(1.5, 1.5):
x = 1.5 and y = 1.5
Since 5(1.5) - 4(1.5) = 1.5, it does satisfy 5x - 4y ≤ C.
(0, 1):
x = 0 and y = 1
Since 5(0) - 4(1) = -4, it does not satisfy 5x - 4y ≤ C.
(0, 0):
x = 0 and y = 0
Since 5(0) - 4(0) = 0, it does satisfy 5x - 4y ≤ C.
Based on these checks, the vertices of the feasible region are (1, 0), (3, 0), (1.5, 1.5), and (0, 0).
To find the vertices of the feasible region for the given objective function, you need to solve the system of inequalities that represent the constraints of the problem. Once you have the solution to the system, the coordinates of the intersection points will give you the vertices.
In this case, since the feasible region is not provided, we'll assume that there are constraints on x and y (such as x ≥ 0 and y ≥ 0). The given objective function is C = 5x - 4y.
To find the vertices using a graphing calculator, follow these steps:
1. Plot the equations or inequalities representing the constraints on the graphing calculator. For example, if the constraints are x ≥ 0 and y ≥ 0, you can graph the lines x = 0 and y = 0.
2. Look for the points where the lines intersect. These intersection points represent the vertices of the feasible region.
3. Using the graphing calculator, identify and select all the vertices of the feasible region. The vertices are the coordinates of the intersection points.
Looking at the list of responses you provided: (0,3), (1,0), (-3,0), (3,0), (1.5,1.5), (0,1), and (0,0), these are the coordinates of the intersection points found when graphing the constraints. It seems that some of the points are repeated in the response.
Note that without knowing the specific constraints and feasible region, it is difficult to determine the accuracy of the provided response.