Question

$\text{Maximize}z=15x_1+20x_2$

$\text{Subject to :}$

$12x_1+4x_2\ge 36$

$12x_1+6x_2\le 24$

$x_1,x_2\ge 0$

$\text{The above linear programming problem has}$

• A. alternative optimum solutions
• B. degenerate solution
• C. infeasible solution
• D. unbounded solution

Answer 1

The correct option is D unbounded solution

$\text{Maximize}z=15x_1+20x_2$

$\text{Subjected to,}$

$12x_1+4x_2\ge 36or3x_1+x_2\ge 9$

$12x_1-6x_2\le 24or2x_1-x_2\le 4$

$\text{Let}$

$3x_1+x_2=9or2x_1-x_2=4$

$x_1=0,x_2=9or{x}_1=0,x_2=-4$

$x_1=3,x_2=0or{x}_1=2,x_2=0$



$\text{Since maximum value of objective function lies at infinity.}$

$\text{So, the problem has an unbounded solution.}$