The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of $Z = 11x + 7y$ is
Answer & explanation
Correct answer: option 1
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 = $21$