The corner points of the bounded feasible region determined by the system of linear constraints of an LPP are (0, 0), (0, 8), (5, 0) and (4, 10). Let \( z=3x-4y \) be the objective function, then the minimum value of \( z \) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −32
For a bounded feasible region, the minimum of z occurs at a corner point. Value of z = 3x − 4y at each corner:
\( \displaystyle (0,0):\ z=0 \)
\( \displaystyle (0,8):\ z=0-32=-32 \)
\( \displaystyle (5,0):\ z=15 \)
\( \displaystyle (4,10):\ z=12-40=-28 \)
The minimum value is −32, at (0, 8).