The feasible region for an LPP is shown by shaded region in the figur…

The correct answer is Option (1) → 21

The shaded region is a triangle with corners (0, 6), (0, 3) and the point where \(x + y = 6\) meets \(x + 3y = 9\). Subtracting the first equation from the second:

    \(2y = 3,\quad y = 1.5\)
\(x = 6 - 1.5 = 4.5\)

By the corner point method, the minimum of Z on this bounded region is at a corner:

    At (0, 6): \(Z = 0 + 42 = 42\)
At (0, 3): \(Z = 0 + 21 = 21\)
At (4.5, 1.5): \(Z = 49.5 + 10.5 = 60\)

So the minimum value of Z is 21, at (0, 3).