If objective function $Z=20x+30y $ of an LPP is subject to the constraints $3x+4y ≥ 12, 4x + y ≥4, x ≥4, x ≥0, y≥ 0, $ then Z has :

(A) Min at (0, 4)

(B) Max at (0, 4)

(C) Min at (4, 0)

(D) Max at (4, 0)

(E) Min at $(\frac{4}{13}, \frac{36}{13})$

Choose the correct answer from the options given below :

(C) Only

The correct answer is Option (1) → (C) Only

$Z_{min}=Z(4,0)$

$=20×4+30×0=80$