Algebra

Linear Programming

Medium

core

The feasible region of the linear programming problem is represented below:

The constraints of this LPP are

$x + y \geq 50, 3x + y \geq 90, x, y \geq 0$

$x + y < 50, 3x + y \leq 90, x, y \geq 0$

$x + y \geq 50, 3x + y \leq 90, x, y \geq 0$

$x + y \geq 50, 3x + y < 90, x, y \geq 0$

✅ Correct Option: 4

Look at the straight line that cuts at $(0,50)$ and $(50,0)$ .

The equation of the line is $x+y=50$ .

The feasible region (shaded region) includes the line and the part above it.

Hence, the constraint it $x+y \geq 50$ .

Now, look at the dashed line which cuts at $(0,90)$ and $(90,0)$ .

The dashed line has the equation $x+y = 90$ .

If it is dashed, the line is not included in the feasible region i.e $(0,90)$ and $(90,0)$ are not part of the feasible region.

The shaded region is below this line.

Hence, the constraint is $x+y<90$ .

Hence, option 4 is the answer.

2025: 15 May Shift 1

Let the corner points of the bounded feasible region of the linear programming problem (LPP) $Z = ax+by$ be: (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between a and b is:

2026: 26 May Shift 2

If the feasible region (shaded portion)of a LPP is as shown in the graph, then max $z = 50x + 15y$ is:

2025: 22 May Shift 2

For LPP: Maximize $z = 2x + 3y$ subject to the constraints

$x + y \geq 2$ , $x + 2y \geq 3$ , $x \geq 0$ , $y \geq 0$ ,

which of the following graph represents the feasible region of the above LPP as shaded portion?

2025: 16 May Shift 1

Consider the following L.P.P.

Minimize z = 400x + 300y subject to 100x + 200y ≥ 12000, 300x + 400y ≥ 20000, 200x + 100y ≥ 15000 and x, y ≥ 0. Then

2026: 30 May Shift 2

The point/points which provides the optimal solution of the linear programming problem maximum $z = 3x+y$ , $x+3y \le 12, 3x+y \le 12, x,y \ge 0$ , is/are

2025: 13 May Shift 1

If corner points of the bounded feasible region are (0, 0), (3, 0) and (0, 3) and objective function is $z = 4x + 7y$ , then the maximum value of $z$ is

The feasible region of the linear programming problem is represented below: The constraints of this LPP are

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The feasible region of the linear programming problem is represented below:

The constraints of this LPP are