To find the values of each vertex in the objective function P=5x+6y and the maximum value, we need to find the coordinates of each vertex of the shaded area.
The three points given are:
Point A: (0, 8)
Point B: (5, 4)
Point C: (9, 0)
To find the coordinates of the vertices, we can look at the x and y coordinates separately.
For the x coordinates:
The x coordinate of the vertex at the left end of the shaded area is 0.
The x coordinate of the vertex at the right end of the shaded area is 9.
For the y coordinates:
The y coordinate of the vertex at the top end of the shaded area is 8.
The y coordinate of the vertex at the bottom end of the shaded area is 0.
So the vertices of the shaded area are:
Vertex A: (0, 8)
Vertex B: (9, 8)
Vertex C: (9, 0)
Vertex D: (0, 0)
Now we can substitute these coordinates into the objective function P=5x+6y to find the values of each vertex:
P(A) = 5(0) + 6(8) = 0 + 48 = 48
P(B) = 5(9) + 6(8) = 45 + 48 = 93
P(C) = 5(9) + 6(0) = 45 + 0 = 45
P(D) = 5(0) + 6(0) = 0 + 0 = 0
The maximum value is 93, which occurs at vertex B.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A Graph with horizontal axis x from left to right labeled from origin intersect 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. vertical axis y labeled from top to bottom 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 and 0. A line is plotted with three points: left parenthesis 0 comma 8 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 9 comma 0 right parenthesis, Area under entire line is gray shaded. What are the values of each vertex in the objective function P=5x+6y What is the maximum value?
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