In a linear programming problem(LPP), the maximum value of the objective function $Z = 2x+5y$ subjected to the constraints: $2x + 3y ≤ 6, 2x + y ≤ 4, x, y ≥0$ is |
12 10 8 4 |
10 |
The correct answer is Option (2) → 10 ** Objective function: $Z = 2x + 5y$ Constraints: $2x + 3y \le 6$ $2x + y \le 4$ $x, y \ge 0$ Corner points of feasible region: $(0,0)$ $(2,0)$ from $2x+y=4$ $(0,2)$ from $2x+3y=6$ $\left(\frac{3}{2},1\right)$ intersection point Evaluate Z at these points: $Z(0,0)=0$ $Z(2,0)=4$ $Z(0,2)=10$ $Z\left(\frac{3}{2},1\right)=3+5=8$ Maximum value is $10$ at $(0,2)$. |