The feasible region for an LPP is shown in the given figure. Let Z=3x…

The correct answer is Option (3) → (C) only

The region is bounded, with corner points at O, on the axes and at the meeting point of the two lines.

    \( 2x+y=104 \) meets the x-axis at (52, 0).

    \( x+2y=76 \) meets the y-axis at (0, 38).

Doubling the first equation and subtracting the second:

    \( 3x=132 \)

    \( x=44,\ y=16 \)

The corner values of Z = 3x + 4y:

    At O(0, 0): Z = 0

    At (52, 0): Z = 156

    At (44, 16): Z = 132 + 64 = 196

    At (0, 38): Z = 152

So the minimum value of Z is 0 (at O) and the maximum value is 196 (at (44, 16)).

Checking the statements

(A) The minimum value of \( Z \) is 156 — Incorrect. The minimum is 0; 156 is the value at (52, 0).

(B) The minimum value of \( Z \) is 152 — Incorrect. The minimum is 0; 152 is the value at (0, 38).

(C) The maximum value of \( Z \) is 196 — Correct. 196 is the largest corner value.

(D) Neither minimum nor maximum value of \( Z \) exists — Incorrect. The region is bounded, so both exist (0 and 196).