Question

If the corner points of the feasible solution are (0, 10), (2, 2), and (4, 0), then the point of minimum \( z = 3x + 2y \) is _______.

• A. (2, 2)
• B. (0, 10)
• C. (4, 0)
• D.

Hint:

In linear programming, evaluate the objective function at all corner points to find the minimum.

Answer 1

The Correct Option is A

Evaluate \( z = 3x + 2y \) at each corner point:
- At (0, 10): \( z = 3 \cdot 0 + 2 \cdot 10 = 20 \).
- At (2, 2): \( z = 3 \cdot 2 + 2 \cdot 2 = 6 + 4 = 10 \).
- At (4, 0): \( z = 3 \cdot 4 + 2 \cdot 0 = 12 \).
Minimum \( z = 10 \) at (2, 2).