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. \( (3, 4) \)

Hint:

In linear programming, the minimum or maximum value of the objective function occurs at the corner points of the feasible region.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
The given linear objective function is \( z = 3x + 2y \). We need to find the minimum value of \( z \) using the feasible corner points. Step 2: Checking each point.
- For \( (0, 10) \), \( z = 3(0) + 2(10) = 20 \). - For \( (2, 2) \), \( z = 3(2) + 2(2) = 12 \). - For \( (4, 0) \), \( z = 3(4) + 2(0) = 12 \). The minimum value occurs at \( (2, 2) \) with \( z = 12 \). Step 3: Conclusion.
Thus, the point of minimum is \( (2, 2) \), so the correct answer is (A).