The minimum value of $Z = 2x + y$ subjected to $x + y ≥ 10,2x + 3y ≤ 26, x, y ≥0$ is

14

The correct answer is Option (1) → 14

Constraints: $x+y\ge 10,\;2x+3y\le 26,\;x\ge 0,\;y\ge 0$.

Intersection points:

$(x+y=10)\cap(2x+3y=26)\Rightarrow (4,6)$

$(x+y=10)\cap(y=0)\Rightarrow (10,0)$

$(2x+3y=26)\cap(y=0)\Rightarrow (13,0)$

Objective $Z=2x+y$ at vertices:

$Z(4,6)=2\cdot 4+6=14$

$Z(10,0)=20,\; Z(13,0)=26$

Minimum value = 14 (attained at $(4,6)$)