The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of $Z = 11x + 7y$ is

21

The correct answer is Option (1) → 21 **

Vertices of feasible region:

$(0,6)$, $(0,3)$, and intersection of $x+y=6$ and $x+3y=9$.

Solving intersection:

$x = 6 - y$

$(6 - y) + 3y = 9$

$2y = 3 \Rightarrow y = 1.5$

$x = 4.5$

Evaluate $Z = 11x + 7y$:

At $(0,6)$: $Z = 42$

At $(0,3)$: $Z = 21$

At $(4.5,1.5)$: $Z = 49.5 + 10.5 = 60$

Minimum value = $21$