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Analyze the Feasible Region:
The feasible region is bounded. We need to determine the inequalities that define this region.
Identify Key Points:
From the image (not provided, but assumed), we can infer two boundary lines. Let's assume the intersection points of these lines with the axes are approximately (0, 38), (104/2, 0) = (52,0), (0, 104), and (76, 0). This suggests the lines are related to the equations x + 2y = 76 and 2x + y = 104.
Determine the Inequalities:
We need to determine whether the inequalities are "greater than or equal to" or "less than or equal to". Since the feasible region is bounded and includes the area "above" the line 2x + y = 104 and "below" the line x + 2y = 76, the inequalities should be:
Consider Non-negativity Constraints:
Since the feasible region is in the first quadrant, we have x ≥ 0 and y ≥ 0.
Match with Options:
Comparing with the given options, the correct set of constraints is:
x + 2y ≤ 76, 2x + y ≥ 104, x, y ≥ 0
Correct Answer: \(x+2y\le76\), \(2x+y\ge104\), \(x, y\ge0\)<\/strong>