Maximize $Z=7 x_{1}-3 x_{2}$ subject to, $x_{1}+2 x_{2} \leq 2,2 x_{1}+4 x_{2} \geq 8, x_{1} \geq 0, x_{2} \geq 0$.

• A

  Unique solution
• B

  Unbounded solution
• Correct answer
  C

  Infeasible solution
• D

  Infinite number of solutions

Solution

We have, $x_{1}+2 x_{2}=2 ; 2 x_{1}+4 x_{2}=8$ i.e., $\quad \frac{x_{1}}{2}+\frac{x_{2}}{1}=1, \frac{x_{1}}{4}+\frac{x_{2}}{2}=1$ The constraint are shown by the graph

From the graph, we conclude that there is no feasible region, i.e. there is no unique solutions satisfying all the constraints.

Hence, the correct answer is option: 'C'.