Question
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. 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)
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GPT 3.5
To find the maximum value of the objective function, we need to evaluate the objective function at each vertex and compare the results.
Given that the objective function is p = 5x + 6y, we can substitute the x and y values of each vertex into the equation to find the corresponding values of p.
1) Vertex (0, 8):
p = 5(0) + 6(8) = 0 + 48 = 48
2) Vertex (5, 4):
p = 5(5) + 6(4) = 25 + 24 = 49
3) Vertex (9, 0):
p = 5(9) + 6(0) = 45 + 0 = 45
Now, we compare the values of p at each vertex:
p at vertex (0, 8) = 48
p at vertex (5, 4) = 49
p at vertex (9, 0) = 45
Therefore, the maximum value of the objective function p = 5x + 6y is 49, which occurs at the vertex (5, 4).
Given that the objective function is p = 5x + 6y, we can substitute the x and y values of each vertex into the equation to find the corresponding values of p.
1) Vertex (0, 8):
p = 5(0) + 6(8) = 0 + 48 = 48
2) Vertex (5, 4):
p = 5(5) + 6(4) = 25 + 24 = 49
3) Vertex (9, 0):
p = 5(9) + 6(0) = 45 + 0 = 45
Now, we compare the values of p at each vertex:
p at vertex (0, 8) = 48
p at vertex (5, 4) = 49
p at vertex (9, 0) = 45
Therefore, the maximum value of the objective function p = 5x + 6y is 49, which occurs at the vertex (5, 4).
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