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)

Answer 1

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).