The feasible region of LPP is shown in the graph : The maximum value…

The correct answer is Option (2) → C

Equation of a line,

$y=mx+c$ [m = slope] [c = constant]

for line connecting (0, 8) and (12, 0)

$y=-\frac{6}{12}x+c$

$y=-\frac{1}{2}x+c$

$⇒2y+x=c$

and,

$2×6+0=c$

$⇒c=12$

$∴2y+x=12$  ...(1)

for line connecting (0, 12) and (6, 0)

$⇒y+2x=12$  ...(2)

Solving (1) and (2),

$2y+4x-(2y+x)=24-12$

$⇒3x=12$

$⇒x=4$ and $y=4$

$Z(4,4)=6×4+4×4$

$=38$ is maximum.