Target Exam

CUET

Subject

Section B2

Chapter

Linear Programming

Question:

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

Options:

12

10

8

4

Correct Answer:

10

Explanation:

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 $(0,2)$.