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The feasible region of a linear programming problem is shown in the figure below: ... Which of the following are the possible constraints?

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Q: The feasible region of a linear programming problem is shown in the figure below: ... Which of the following are the possible constraints?

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Analyze the graph:<\/strong> The feasible region is bounded by lines. We need to determine the inequalities that define this region.

Consider the line x + 2y = 4:<\/strong> The line passes through (4,0) and (0,2). The feasible region lies above this line. Therefore, the inequality is x + 2y ≥ 4.

Consider the line x + y = 3:<\/strong> The line passes through (3,0) and (0,3). The feasible region lies below this line. Therefore, the inequality is x + y ≤ 3.

Consider the non-negativity constraints:<\/strong> Since the feasible region is in the first quadrant, x ≥ 0 and y ≥ 0.

Combine the inequalities:<\/strong> The constraints are x + 2y ≥ 4, x + y ≤ 3, x ≥ 0, and y ≥ 0.

Match with the options:<\/strong> Option (A) matches the derived constraints: x + 2y ≥ 4, x + y ≤ 3, x ≥ 0, y ≥ 0.

Correct Answer: x+2y\ge4, x+y\le3, x\ge0, y\ge0

AI Suggestion: Option A

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