Question

For $L.P.P$, maximize $z = 4x_{1}+ 2x_{2}$ subject to $3x_{1} + 2x_{2} \ge 9, x_{1} - x_{2} \le 3, x_{1} \ge 0, x_{2} \ge 0$ has .........

• A. infinite number of optimal solutions
• B. unbounded solution
• C. no solution
• D. one optimal solution

Answer 1

Answer: (B)

We have, maximise $z=4 x_{1}+2 x_{2}$
Subject to constracts, $3 x_{1}+2 x_{2} \geq 9, x_{1}-x_{2} \leq 3$
$x_{1} \geq 0, x_{2} \geq 0$
On taking given constraints as equation, we get the following graphs

Here, we get feasible region Is unbounded.