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What kind of region is described by the inequalities x ≥ 0, y ≥ 0, x + y ≤ 6, and x + y ≤ 3?

1. An unbounded region in the first quadrant
2. A bounded region extending into the first and second quadrants
3. A bounded region in the first quadrant
4. None of the above

Correct answer: A bounded region in the first quadrant

Solution

The inequalities define a region that is limited by the lines x + y = 6 and x + y = 3, both of which intersect the axes in the first quadrant, creating a bounded area where both x and y are non-negative.

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