For a linear programming problem, the maximum value of the objective function \( z=2x+3y \) subject to constraints:
\( x-y\le -1,-x+y\le 0,x,y\ge 0 \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Maximum value does not exist.
The first two constraints give
\( \displaystyle x-y\le -1\ \Rightarrow\ y\ge x+1 \)
\( \displaystyle -x+y\le 0\ \Rightarrow\ y\le x \)
A point satisfying both would need \( x+1\le y\le x \), i.e. \( 1\le 0 \), which is impossible. Graphically, y = x + 1 and y = x are parallel lines and the two half-planes do not overlap.
So there is no feasible region: no point satisfies all the constraints, and z has no maximum value.