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Question
Choose the correct alternative :
The corner points of the feasible region given by the inequations x + y ≤ 4, 2x + y ≤ 7, x ≥ 0, y ≥ 0, are
Options
(0, 0), (4, 0), (3, 1), (0, 4).
(0, 0), `(7/2, 0)`, (3, 1), (0, 4).
(0, 0), `(7/2, 0), (3, 1)`, (5, 7).
(6, 0), (4, 0), (3, 1), (0, 7).
Solution
Given inequalities are x + y ≤ 4, 2x + y ≤ 7.
Consider line L1 : x + y = 4 and L2 : 2x + y = 7
For line L1, A (0, 4) and B (4, 0)
For line L2, P(0, 7) and Q`(7/2, 0)`
Solving both lines, we get x = 3, y = 1.
The coordinates of origin O (0, 0) satisfies both the inequalities.
∴ The required region is on the origin side of both the lines L1 and L2.
As x ≥ 0, y ≥ 0, the feasible region is in the first quadrant.
OQRAO is the required feasible region.
∴ The corner points are O (0, 0), Q`(7/2, 0)`, R (3, 1), A (0, 4).
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