Question

Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:

• A. Only $(0, 2)$
• B. Only $(3, 0)$
• C. The mid-point of the line segment joining the points $(0, 2)$ and $(3, 0)$
• D. Any point on the line segment joining the points $(0, 2)$ and $(3, 0)$

Answer 1

The Correct Option is D

The feasible region is bounded, and $z = 4x + 6y$ is the objective function. Compute $z$ at the corner points: \[ z(0, 2) = 12, \quad z(3, 0) = 12. \] Since $z$ has the same value at $(0, 2)$ and $(3, 0)$, any point on the line segment joining these points also gives the minimum value of $z$.