The feasible region for a LPP is shown in the figure. The minimum value of \( Z=2x-3y \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −12
The feasible region is bounded, so the minimum of \( Z=2x-3y \) occurs at a corner point. The corner values are:
\( \mathrm{O}(0,0):\ Z=0 \)
\( \mathrm{A}(0,2):\ Z=-6 \)
\( \mathrm{B}(1.5,5):\ Z=-12 \)
\( \mathrm{C}(4,3.5):\ Z=-2.5 \)
\( \mathrm{D}(3,0):\ Z=6 \)
The minimum value is −12, at B(1.5, 5).
Why the other options are incorrect
Option (1) −6 — Incorrect. This is the value at A(0, 2), which is not the smallest corner value.
Option (3) −2 — Incorrect. No corner gives −2; the minimum is −12.
Option (4) 6 — Incorrect. This is the maximum value, at D(3, 0), not the minimum.