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
Answer & explanation
Correct answer: option 2
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 $(0,2)$.