If the corner points of the bounded feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of the objective function \( z=2x+3y \) occurs 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 )
The values of z = 2x + 3y at the corner points are
At (0, 2): z = 6
At (3, 0): z = 6
At (6, 0): z = 12
At (6, 8): z = 36
At (0, 5): z = 15
The minimum value 6 occurs at two adjacent corners, (0, 2) and (3, 0). In that case z has the same minimum value at every point of the edge joining them.
NCERT Exemplar:
Linear Programming
