To determine which ordered pair maximizes the objective function p = 3x + 8y, we will evaluate this function at the given points: (0, 0), (2, 7), (5, 6), and (8, 1).
1. For the point (0, 0):
p = 3(0) + 8(0) = 0
2. For the point (2, 7):
p = 3(2) + 8(7) = 6 + 56 = 62
3. For the point (5, 6):
p = 3(5) + 8(6) = 15 + 48 = 63
4. For the point (8, 1):
p = 3(8) + 8(1) = 24 + 8 = 32
Now, we can compare the values of p obtained from each ordered pair:
- At (0, 0), p = 0
- At (2, 7), p = 62
- At (5, 6), p = 63
- At (8, 1), p = 32
The maximum value of p is 63, which occurs at the point (5, 6).
Therefore, the ordered pair that maximizes the objective function is (5, 6).