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Question
The region represented by the inequation system x, y ≥ 0, y ≤ 6, x + y ≤ 3 is
Options
unbounded in first quadrant
unbounded in first and second quadrants
bounded in first quadrant
none of these
Solution
bounded in first quadrant
Converting the given inequations into equations, we obtain
\[y = 6, x + y = 3, x = 0 \text{ and }y = 0\] y = 6 is the line passing through (0, 6) and parallel to the X axis.The region below the line y = 6 will satisfy the given inequation.
The line x + y = 3 meets the coordinate axis at A(3, 0) and B(0, 3). Join these points to obtain the line x + y =3.
Clearly, (0, 0) satisfies the inequation x + y ≤ 3. So, the region in xy-plane that contains the origin represents the solution set of the given equation.
Region represented by x ≥ 0 and y ≥ 0:
Since, every point in the first quadrant satisfies these inequations. So, the first quadrant is the region represented by the inequations.
These lines are drawn using a suitable scale.
The shaded region represents the feasible region of the given LPP, which is bounded in the first quadrant
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