While solving an LPP, the corner points of a bounded feasible region were found to be (0,0), (1, 9), (3, 7), (4, 5.5) and (10, 0). The objective function Z = 4x + y will maximise at:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (10, 0)
The region is bounded, so the maximum of Z is at one of the corner points. Value of \( Z=4x+y \) at each corner:
\( \displaystyle (0,0):\ Z=0 \)
\( \displaystyle (1,9):\ Z=4+9=13 \)
\( \displaystyle (3,7):\ Z=12+7=19 \)
\( \displaystyle (4,5.5):\ Z=16+5.5=21.5 \)
\( \displaystyle (10,0):\ Z=40+0=40 \)
The largest value is 40, at (10, 0).