The feasible region for a linear programming problem is shown in the figure.
Let \( Z=3x-4y \) be the objective function, then minimum of Z occurs at the point
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → D
The feasible region is bounded, so by the corner point method the minimum of Z occurs at a corner point. The values of \( Z=3x-4y \) at the corners are:
\( O(0,0):\ Z=0 \)
\( A(5,0):\ Z=15-0=15 \)
\( B(6,8):\ Z=18-32=-14 \)
\( C(4,10):\ Z=12-40=-28 \)
\( D(0,8):\ Z=0-32=-32 \)
The smallest value is −32, at D(0, 8).