The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (0, 9), (2, 10), (6, 8), (10, 0). If the objective function is \( Z=6x+5y \), then (Maximum value of \( Z \) – Minimum value of \( Z \)) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 76
The region is bounded, so the extreme values of \( Z=6x+5y \) occur at corner points:
\( \displaystyle (0,0):\ Z=0 \)
\( \displaystyle (0,9):\ Z=45 \)
\( \displaystyle (2,10):\ Z=62 \)
\( \displaystyle (6,8):\ Z=76 \)
\( \displaystyle (10,0):\ Z=60 \)
The maximum is 76 and the minimum is 0.
\( \displaystyle 76-0=76 \)