The corner points of the bounded feasible region of a linear programming problem are (0, 0), (0, 8), (2, 7), (5, 4) and (6, 0). The maximum profit \( P=3x+2y \) occurs at the point
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (5, 4)
For a bounded feasible region the maximum occurs at a corner point. The values of P at the corners are:
\( \displaystyle (0,0):\ P=0 \)
\( \displaystyle (0,8):\ P=16 \)
\( \displaystyle (2,7):\ P=6+14=20 \)
\( \displaystyle (5,4):\ P=15+8=23 \)
\( \displaystyle (6,0):\ P=18 \)
The largest value is 23, at (5, 4).