The corner points of the bounded feasible region for an LPP are (0, 0), (6, 0), (4, 3) and (0, 8). The objective function \( Z=px+qy,\ p,q\gt 0 \) has maximum value 360 at points (6, 0) and (4, 3). The value of \( Z \) at (0, 8) is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 320
The maximum value 360 is reached at both (6, 0) and (4, 3):
\( \displaystyle Z(6,0)=6p=360 \)
\( \displaystyle p=60 \)
\( \displaystyle Z(4,3)=4p+3q=360 \)
\( \displaystyle 240+3q=360 \)
\( \displaystyle q=40 \)
\( \displaystyle Z(0,8)=8q=8\times 40=320 \)
Check: 320 < 360, consistent with 360 being the maximum.