Question

The vertices of a feasible region are (0,0), (0,2.5), (3,1), and (2,0). For which objective function is the maximum cost (C) found at the vertex (3,1)? A) C = -3x + 2y B) C = 3x + 2y C) C = 4x - 2y D) C = x + 5y

Answer 1

The objective function that gives the maximum cost at the vertex (3,1) is B) C = 3x + 2y, with a value of 11.

Step-by-step explanation:

To determine which objective function has its maximum cost (C) at the vertex (3,1), we need to evaluate each given function at all vertices points and see which function yields the highest value at the point (3,1).

• Evaluate A) C = -3x + 2y at (3,1): C = -3(3) + 2(1) = -9 + 2 = -7
• Evaluate B) C = 3x + 2y at (3,1): C = 3(3) + 2(1) = 9 + 2 = 11
• Evaluate C) C = 4x - 2y at (3,1): C = 4(3) - 2(1) = 12 - 2 = 10
• Evaluate D) C = x + 5y at (3,1): C = 1(3) + 5(1) = 3 + 5 = 8

The function that gives the highest value at the vertex (3,1) is B) C = 3x + 2y, which gives a value of 11. Therefore, the maximum cost (C) is found at the vertex (3,1) for the objective function B) C = 3x + 2y.