Question

Linear Programming Question: Which of the following vertices would minimize the objective function N = 7x + 2y?

a) (0, 12)
b) (6, 3)
c) (3, 9)
d) (4, 0)

Answer 1

The vertex that minimizes the objective function N = 7x + 2y is (0, 12), with N = 24.

Step-by-step explanation:

To determine which vertex minimizes the objective function N = 7x + 2y, we can simply calculate N for each of the given vertices:

• For vertex (0, 12): N = 7(0) + 2(12) = 24
• For vertex (6, 3): N = 7(6) + 2(3) = 42 + 6 = 48
• For vertex (3, 9): N = 7(3) + 2(9) = 21 + 18 = 39
• For vertex (4, 0): N = 7(4) + 2(0) = 28

The vertex that gives the minimum value for N is (0, 12), which results in N = 24. Therefore, the answer is a) (0, 12).