The minimum value of $Z = 3x + 2y$ subjected to the constraints $2x + y ≥7,x + 2y ≥8;x, y ≥ 0$ is

12

The correct answer is Option (3) → 12 **

Feasible region comes from the constraints:

$2x+y\ge 7,\; x+2y\ge 8,\; x\ge 0,\; y\ge 0$

Evaluate $Z=3x+2y$ at all feasible corner points:

At $(0,7)$: $Z=3(0)+2(7)=14$

At $(8,0)$: $Z=3(8)+2(0)=24$

At $(2,3)$: $Z=3(2)+2(3)=12$

The minimum value of $Z$ is $12$.