Discussion
The feasible region represented by the constraints \(x_{1} - x_{2} \le 1\), \(x_{1} + x_{2} \ge 3\), \(x_{1} \ge 0\), \(x_{2} \ge 0\) of the objective function Max \(Z = 3x_{1} + 2x_{2}\) is
Answer: B
The constraints are \(x_{1} - x_{2} \le 1\), \(x_{1} + x_{2} \ge 3\) and both variables non-negative. Along the line \(x_{1} - x_{2} = 1\), the point \((x_{2} + 1, x_{2})\) satisfies the second constraint once \(x_{2} \ge 1\) and can be taken as large as one pleases, so the feasible region extends without limit and no constraint closes it. It is therefore an unbounded feasible region, option (B), not a polygon or a single point, which are bounded.
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