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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
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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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