Question

The shaded region in the following figure represents the solution set for a certain linear programming problem. Then linear constraints for this region are given by}

• A. $x \ge 0, y \ge 0, x+y \le 4, x+3y \ge 6$
• B. $x \ge 0, y \ge 0, x+y \ge 4, x+3y \le 6$
• C. $x \le 0, y \le 0, x+y \le 4, x+3y \ge 6$
• D. $x \ge 0, y \ge 0, x+y \ge 4, x+3y \ge 6$

Hint:

To find linear constraints from a shaded region: (1) Identify the axes ($x \ge 0, y \ge 0$ for the first quadrant). (2) For each boundary line, find its equation (e.g., using two points or intercepts). (3) Test a point within the shaded region (or the origin if it's not in the region) to determine the correct inequality direction ($\le$ or $\ge$).

Answer 1

The Correct Option is A