Mathematics

Mathematics

Problem

The inequalities below are graphed together: (i) x+y≥3x + y \ge 3 (ii) x≥0x \ge 0 (iii) y≥0y \ge 0 Which additional inequality, when added as a fourth condition, will make the feasible region empty? a) x+y≤3x + y \le 3 b) x≤0x \le 0 c) x+y≤2x + y \le 2 d) x+y≥5x + y \ge 5
Intuitive explanation

The feasible region is currently a bounded area in the first quadrant above the line x+y=3x + y = 3. To make it empty, you need an inequality that contradicts what's already required—think about what constraint would force points to be somewhere they're forbidden to go. The key is finding a boundary that cuts off all points satisfying the first three conditions simultaneously.

Intuitive explanation

The feasible region is currently a bounded area in the first quadrant above the line x+y=3x + y = 3. To make it empty, you need an inequality that contradicts what's already required—think about what constraint would force points to be somewhere they're forbidden to go. The key is finding a boundary that cuts off all points satisfying the first three conditions simultaneously.

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