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Question
Find the linear inequalities for which the shaded region in the given figure is the solution set.
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Solution
Considering 3x + 2y = 48,
The shaded region and the origin both are on the same side of the graph of the line and (0, 0) satisfy the constraint 3x + 2y ≤ 48.
Considering x + y = 20,
The shaded region and the origin both are on the same side of the graph of the line and (0, 0) satisfy the constraint x + y ≤ 20.
We also know that, Shaded region is in the first quadrant i.e. x ≥ 0 and y ≥ 0.
Hence, the linear inequalities are 3x + 2y ≤ 48, x + y ≤ 20, x ≥ 0, y ≥ 0.
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