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