To determine which ordered pair maximizes the objective function p = 3x + 8y, we need to evaluate the function for each of the given pairs:
- For (0, 0): p = 3(0) + 8(0) = 0
- For (2, 7): p = 3(2) + 8(7) = 6 + 56 = 62
- For (5, 6): p = 3(5) + 8(6) = 15 + 48 = 63
- For (8, 1): p = 3(8) + 8(1) = 24 + 8 = 32
Comparing the results, we find:
- (0, 0) gives: 0
- (2, 7) gives: 62
- (5, 6) gives: 63
- (8, 1) gives: 32
Hence, the ordered pair that maximizes the objective function p = 3x + 8y is (5, 6), with a maximum value of 63.