Choose the correct alternative : The corner points of the feasible region given by the inequations x + y $\leq$ 4, 2x + y $\leq$ 7, x $\geq$ 0, y $\geq$ 0, are

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Given inequalities are x + y $\leq$ 4, 2x + y $\leq$ 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($\frac{7}{2}$, 0) Solving both lines, we get x = 3, y = 1. The coordinates of origin O (0, 0) satisfies both the inequalities. $\therefore$ The required region is on the origin side of both the lines L1 and L2. As x $\geq$ 0, y $\geq$ 0, the feasible region is in the first quadrant. OQRAO is the required feasible region. $\therefore$ The corner points are O (0, 0), Q($\frac{7}{2}$, 0), R (3, 1), A (0, 4).

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