Solve the following Linear Programming Problem graphically: Maximize $Z=3x+4y$ Subject to $x+y≤4,x≥0$ and $y≥0$.

16

The correct answer is Option (3) → 16

The feasible region is a triangle with vertices $O(0,0), A(4,0)$ and $B(0,4)$

$Z_O=3×0+4×0=0$

$Z_A=3×4+4×0=12$

$Z_B=3×0+4×4=16$

Thus, maximum of Z is at B(0, 4) and the maximum value is 16.