Discussion
Consider the following LP problem.
Max \(Z = 6x_{1} - 4x_{2}\)
Subject to the constraints :
\(2x_{1} + 4x_{2} \le 4\)
\(4x_{1} + 8x_{2} \ge 16\)
\(x_{1}, x_{2} \ge 0\).
Then L.P. has :
Answer: A
The LP has an infeasible solution, that is, no feasible solution.
Divide the constraints by 2 and by 4:
\[ \begin{aligned} x_{1} + 2x_{2} &\le 2 \\ x_{1} + 2x_{2} &\ge 4 \end{aligned} \]
No point can make the same expression at most 2 and at least 4, so the feasible region is empty. Without a feasible point there is no basic feasible solution and no unbounded solution either, which rules out B, C and D.
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