What are the values of each vertex in the objective function P=5x+6y
What is the maximum value? Constraints: (0,8) (5,4) (9,0)
In the objective function P = 5x + 6y, the values of x and y represent the variables that we can adjust to optimize the objective function.
To find the values of each vertex in the objective function, we need to substitute the x and y coordinates of each vertex into the objective function.
Vertex (0,8):
P = 5(0) + 6(8) = 0 + 48 = 48
Vertex (5,4):
P = 5(5) + 6(4) = 25 + 24 = 49
Vertex (9,0):
P = 5(9) + 6(0) = 45 + 0 = 45
Therefore, the values of the objective function at each vertex are:
- Vertex (0,8): P = 48
- Vertex (5,4): P = 49
- Vertex (9,0): P = 45
To find the maximum value, we compare the values at each vertex. The maximum value is therefore 49, which occurs at the vertex (5,4).
To find the values of each vertex in the objective function P = 5x + 6y, we need to substitute the x and y values of each vertex into the equation.
Given the vertices: (0,8), (5,4), and (9,0)
For the vertex (0,8):
P = 5(0) + 6(8) = 0 + 48 = 48
For the vertex (5,4):
P = 5(5) + 6(4) = 25 + 24 = 49
For the vertex (9,0):
P = 5(9) + 6(0) = 45 + 0 = 45
The values of each vertex in the objective function are:
(0,8) -> P = 48
(5,4) -> P = 49
(9,0) -> P = 45
To find the maximum value, we compare the P values for each vertex.
The maximum value is 49, which occurs at the vertex (5,4).
To find the values of each vertex in the objective function P=5x+6y, we need to substitute the x and y values of each vertex into the objective function P and calculate the result.
Let's start with the first vertex (0,8):
Substituting x=0 and y=8 into the objective function:
P = 5(0) + 6(8) = 0 + 48 = 48
Next, let's move to the second vertex (5,4):
Substituting x=5 and y=4 into the objective function:
P = 5(5) + 6(4) = 25 + 24 = 49
Finally, let's calculate the objective function for the third vertex (9,0):
Substituting x=9 and y=0 into the objective function:
P = 5(9) + 6(0) = 45 + 0 = 45
So, the values of each vertex in the objective function are:
- Vertex (0,8): P = 48
- Vertex (5,4): P = 49
- Vertex (9,0): P = 45
Now let's determine the maximum value. In this case, we can compare the values we obtained for each vertex. The maximum value is the highest value among the three calculated values.
Here, the highest value is 49 (from the vertex (5,4)).
Therefore, the maximum value of the objective function P=5x+6y, considering the given constraints, is P = 49.