what are the values of each vertex in the objective function
p=5x+6y
what is the maximum value
(0,8) (5,4) (9,0)
To find the values of each vertex in the objective function, we substitute the x and y coordinates into the objective function p=5x+6y.
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 maximum value among the vertices is 49, which occurs at the vertex (5,4).
To find the values of each vertex in the objective function, p=5x+6y, you can substitute the given points into the equation and calculate the value of p.
Substituting the coordinates (0,8) into the equation:
p = 5(0) + 6(8)
p = 0 + 48
p = 48
Substituting the coordinates (5,4) into the equation:
p = 5(5) + 6(4)
p = 25 + 24
p = 49
Substituting the coordinates (9,0) into the equation:
p = 5(9) + 6(0)
p = 45 + 0
p = 45
So, 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, you compare the values of p at each vertex. In this case, the maximum value is p = 49, which occurs at the vertex (5,4).
To find the values of each vertex in the objective function p=5x+6y, we substitute the x and y coordinates of each vertex into the equation.
Let's substitute the x and y values for each vertex and find the corresponding values of p.
For the first vertex (0,8):
p = 5(0) + 6(8)
p = 0 + 48
p = 48
For the second vertex (5,4):
p = 5(5) + 6(4)
p = 25 + 24
p = 49
For the third vertex (9,0):
p = 5(9) + 6(0)
p = 45 + 0
p = 45
Therefore, the values of p for each vertex are as follows:
- (0,8) has a value of 48
- (5,4) has a value of 49
- (9,0) has a value of 45
To determine the maximum value, we compare these values. In this case, the maximum value is 49, which is obtained at the vertex (5,4).