Question

The point which does not belong to the feasible region of the LPP:
Minimize: $Z=60x+10y$
subject to $3x+y\ge 18$
$2x+2y\ge 12$
$x+2y\ge 10$
$x,y\ge 0$ is

• A. $(0,8)$
• B. $(4,2)$
• C. $(6,2)$
• D. $(10,0)$

Answer 1

The correct option is B $(4,2)$

We test whether the inequalitiies are satisfied or not
$(0,8)$, $3\left(0\right)+8\ge 8$ $8\ge 8$ is true.
$2\left(0\right)+2\left(8\right)=16\ge 12$ is true.
$0+2\left(8\right)=16\ge 10$ is true.
$\therefore$ $(0,8)$ is in the feasible region.
$(4,2)$, $3\left(4\right)+2=14\ge 8$
$2\left(4\right)+2\left(2\right)=16\ge 12$
$4+2\left(2\right)=8\ge 10$ is not true
$\therefore$ $(4,2)$ is not a point in the feasible region
$\therefore$ (2) is correct