The minimum value of $Z = 3x + 2y$ subjected to the constraints $2x + y ≥7,x + 2y ≥8;x, y ≥ 0$ is
Answer & explanation
Correct answer: option 3
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 $12$.
