If the corner points of bounded feasible region for an LPP are (0, 2) (3, 0) (6, 0) (6, 8) and (0, 5) then the minimum value of the objective function \(f=4x+6y\) occur at
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Every point on the line segment joining the points (0, 2) and (3, 0)
By the corner point method, the values of f = 4x + 6y at the corners are
\((0, 2): f = 12\)
\((3, 0): f = 12\)
\((6, 0): f = 24\)
\((6, 8): f = 72\)
\((0, 5): f = 30\)
The minimum value 12 occurs at two adjacent corners, (0, 2) and (3, 0). Every point of the segment joining them lies on the line 4x + 6y = 12, so f = 12 at each of these points as well.
So the minimum occurs at every point of that segment, not at one point only.
NCERT Exemplar:
Linear Programming
