Question

The minimum value for the LPP \( Z = 6x + 2y \), subject to \( 2x + y \geq 16, x \geq 6, y \geq 1 \) is

• A. 44
• B. 47
• C. 24
• D. 34

Hint:

In LPP problems, always identify the feasible region by solving the system of inequalities and then compute the objective function at the feasible points.

Answer 1

The Correct Option is A

Step 1: Use the LPP constraints.
The constraints are: \[ 2x + y \geq 16, \quad x \geq 6, \quad y \geq 1 \] We need to find the feasible region and the minimum value of \( Z = 6x + 2y \). Step 2: Check the feasible points.
The feasible points are found by solving the system of inequalities, which gives the minimum value of \( Z = 44 \) at the point \( (6, 4) \).
Step 3: Conclusion.
The correct answer is (A) 44.