Question

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

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

Answer 1

Answer: (D)

any point on the line segment joining the points $(0,2)$ and $(3, 0)$

Answer 2

Construct the following table of values of objective function: Since the minimum value $(F) = 12$ occurs at two distinct corner points, it occurs at every point of the segment joining these two points.