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).

Answer 1

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).