Find the maximum value of the objective function $Z=3x+4y$ subject to the constraints $x+y\le 4$, $x\ge 0$, $y\ge 0$.

Solution

1. The corner points of the feasible region defined by $x+y\le 4$, $x\ge 0$, $y\ge 0$ are $(0,0)$, $(4,0)$, and $(0,4)$.
2. Evaluate $Z=3x+4y$ at $(0,0)$ to get $Z=0$.
3. Evaluate $Z=3x+4y$ at $(4,0)$ to get $Z=12$.
4. Evaluate $Z=3x+4y$ at $(0,4)$ to get $Z=16$.
5. Hence the answer is (B).