Question

Consider the following linear programming problem (LPP):

$\text{Maximize}z=5x_1+3x_2$

Subjected to the following constraints
$x_1-x_2\le 2x_1+x_2\ge 3x_1,x_2\ge 0$

The above LPP has

• A. no solution
• B. unbounded solution
• C. unique solution
• D. two solutions

Answer 1

The correct option is B unbounded solution

$Z_{max}=5x_1+3x_2$

$\text{Subjected to,}$

$x_1-x_2\le 2$

$x_1+x_2\ge 3$

$x_1,x_2\ge 0$

$\frac{x_1}{1}+\frac{x_2}{-2}\le 1$

$\frac{x_1}{3}+\frac{x_2}{3}\ge 1$


Unbounded solution will exist as it is a case of maximization.