Algebra

Linear Programming

Medium

common

The feasible region represented by the constraints: $x + 2y \geq 100$ , $2x - y \leq 0$ , $2x + y \leq 200$ , $x \geq 0$ , $y \geq 0$ of an LPP is:

Region A

Region B

Region C

Region D

✅ Correct Option: 3

The feasible region is where all constraints are satisfied simultaneously.

For the constraint $x + 2y \geq 100$ :

Draw the line $x + 2y = 100$

The region satisfying this constraint is above or on this line.

For the constraint $2x - y \leq 0$ :

Rearranging: $y \geq 2x$

Draw the line $y = 2x$

The region satisfying this constraint is above or on this line.

For the constraint $2x + y \leq 200$ :

Draw the line $2x + y = 200$

The region satisfying this constraint is below or on this line.

For the constraints $x \geq 0$ and $y \geq 0$ :

The region must be in the first quadrant.

The feasible region must satisfy all conditions:

Above the line $x + 2y = 100$
Above the line $y = 2x$
Below the line $2x + y = 200$
In the first quadrant

Looking at the diagram, Region C is the only region that satisfies all five constraints.

Region A does not satisfy $x + 2y \geq 100$

Region B does not satisfy $y \geq 2x$

Region D does not satisfy $2x + y \leq 200$

Therefore, the feasible region is Region C.

2025: 30 May Shift 1

The corner points of the bounded feasible region for an LPP are (0, 20), (3,12), (6,8), and (0,15). The objective function is $Z = \alpha x + \beta y$ , where $\alpha, \beta > 0$ . If the maximum of Z occurs at the corner points (3,12) and (6,8), then the relationship between $\alpha$ and $\beta$ is:

2025: 30 May Shift 1

If the corner points of the bounded feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of objective function F = 4x + 6y occurs at

2026: 21 May Shift 2

The corner points of the bounded feasible region for an LPP are $(0,5), (6,6), (9,9)$ and $(0,12)$ . If the objective function is $Z = px + qy; p,q>0$ , then the condition on $p$ and $q$ so that the maximum of $Z$ occurs at $(9,9)$ and $(0,12)$ is

2025: 14 May Shift 2

The maximum value of the objective function $Z = 2x + y$ of an LPP, subject to the constraints $x \leq 6, y \leq 2, x - y \leq 0$ , $x \geq 0, y \geq 0$ is

2026: 30 May Shift 2

Consider the linear programming problem (LPP):

Max Z= 4x + 3y

subject to the constraints:

$x\le 8, y\le 4, x\ge 0, y\ge 0$ . At what coordinates will the objective function have optimal solution?

2022: 7 Aug Shift 2

The solution of LPP

max.(z) = $5x + 3y$ subject to

$2x + y \leq 6$

$x + y \leq 4$

$x \geq 0, y \geq 0$ , is

The feasible region represented by the constraints: x+2y≥100x + 2y \geq 100x+2y≥100, 2x−y≤02x - y \leq 02x−y≤0, 2x+y≤2002x + y \leq 2002x+y≤200, x≥0x \geq 0x≥0, y≥0y \geq 0y≥0 of an LPP is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The feasible region represented by the constraints: $x + 2y \geq 100$ , $2x - y \leq 0$ , $2x + y \leq 200$ , $x \geq 0$ , $y \geq 0$ of an LPP is: