If the objective function for a linear programming problem (LPP) is \(Z = 4x + 5y\) and the corner points of the bounded feasible region are (9, 0), (4, 3), (2, 5), and (0, 8), then the minimum value of Z is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 31
On a bounded feasible region, the minimum of Z occurs at a corner point:
\(Z(9, 0) = 36\)
\(Z(4, 3) = 16 + 15 = 31\)
\(Z(2, 5) = 8 + 25 = 33\)
\(Z(0, 8) = 40\)
The smallest corner value is 31, at (4, 3).
Why the other options are incorrect
Option (1) 0 — Incorrect. Z = 0 only at (0, 0), which is not a corner point of this region.
Option (3) 36 — Incorrect. This is Z at (9, 0), not the smallest corner value.
Option (4) 40 — Incorrect. This is the maximum of Z, at (0, 8).