X>0 y>0-x+3>y y<1/3x+1
Use the following constraints and objective function to answer the next 3 questions. 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)
What is the maximum value for C
To find the maximum value for C, we need to evaluate the objective function at each vertex of the feasible region.
The vertices of the feasible region are (-3,0), (0,0), (0,1), and (1.5,1.5).
Evaluating the objective function at each vertex:
At (-3,0): C = 5(-3) - 4(0) = -15
At (0,0): C = 5(0) - 4(0) = 0
At (0,1): C = 5(0) - 4(1) = -4
At (1.5,1.5): C = 5(1.5) - 4(1.5) = 3
Therefore, the maximum value for C is 3.
To find the maximum value for the objective function C=5x−4y, we need to evaluate the objective function at each vertex of the feasible region and select the maximum value.
The vertices of the feasible region are (0,3), (1,0), (-3,0), (3,0), and (1.5,1.5).
We can substitute the coordinates of each vertex into the objective function to find the corresponding values of C:
C(0,3) = 5(0) - 4(3) = -12
C(1,0) = 5(1) - 4(0) = 5
C(-3,0) = 5(-3) - 4(0) = -15
C(3,0) = 5(3) - 4(0) = 15
C(1.5,1.5) = 5(1.5) - 4(1.5) = 1.5
The maximum value for C is 15, which occurs at the point (3,0).
To find the maximum value for C, we need to evaluate the objective function at each vertex of the feasible region and compare the results.
From the responses provided, the vertices of the feasible region are:
- (0,3)
- (1,0)
- (-3,0)
- (3,0)
- (1.5,1.5)
- (0,1)
- (0,0)
Now we can substitute the x and y coordinates of each vertex into the objective function C = 5x - 4y and calculate the result:
For (0,3):
C = 5(0) - 4(3) = -12
For (1,0):
C = 5(1) - 4(0) = 5
For (-3,0):
C = 5(-3) - 4(0) = -15
For (3,0):
C = 5(3) - 4(0) = 15
For (1.5,1.5):
C = 5(1.5) - 4(1.5) = 1.5
For (0,1):
C = 5(0) - 4(1) = -4
For (0,0):
C = 5(0) - 4(0) = 0
Based on these calculations, the maximum value for C is 15, which occurs at the vertex (3,0).