The maximum value of the objective function \(z = 2x + 3y\) of an L.P.P. subjected to the constraints \(x-y \le 1, x + y \le 3, x, y \ge 0\), is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9
The feasible region lies in the first quadrant, below x + y = 3 and above x − y = 1. The lines x − y = 1 and x + y = 3 meet where
\(2x = 4,\quad x = 2,\quad y = 1\)
So the corner points are (0, 0), (1, 0), (2, 1) and (0, 3). By the corner point method:
\(z(0, 0) = 0\)
\(z(1, 0) = 2\)
\(z(2, 1) = 4 + 3 = 7\)
\(z(0, 3) = 9\)
The region is bounded, so the maximum value is 9, at (0, 3).