The feasible region of an LPP is shown in the figure below.
If \(z = 3x + 9y\), then the minimum value of z occurs at :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (5, 5)
The feasible region is bounded, so the minimum of z occurs at a corner point. Its corner points are (0, 10), (0, 20), (15, 15) and (5, 5).
Values of z = 3x + 9y at the corners:
\(z(0, 10) = 0 + 90 = 90\)
\(z(0, 20) = 0 + 180 = 180\)
\(z(15, 15) = 45 + 135 = 180\)
\(z(5, 5) = 15 + 45 = 60\)
The smallest value is 60, so the minimum of z occurs at (5, 5).
NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems
