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For the region determined by the inequalities 3x + 4y ≤ 18, 2x + 3y ≥ 3, and x ≥ 0, y ≥ 0, which of the following is a vertex of the feasible set?

1. (0, 2)
2. (4, 8, 0)
3. (0, 3)
4. None of these

Correct answer: None of these

Solution

The feasible region's corners come from intersecting the boundary lines. They are (0,1) [x=0 & 2x+3y=3], (0,4.5) [x=0 & 3x+4y=18], (1.5,0) and (6,0) [y=0 cases]. Neither (0,2) nor (0,3) is a vertex, and (4,8,0) is malformed, so none of these is correct.

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