Algebra

Linear Programming

Medium

common

Which one of the following represents the correct feasible region determined by the following constraints

$x - y \geq 5$ , $5x - 5y \leq 16$

✅ Correct Option: 1

For the line $x - y = 5$ (passes through $(5,0)$ and $(0,-5)$ ):
- Inequality: $x - y \ge 5$
- Testing $(0,0)$ : $0 - 0 \ge 5 \implies 0 \ge 5$ (False).
- This means the region must be on the side away from the origin. Looking at the line passing through $(5,0)$ , the origin is to its upper-left. So "away from the origin" means shading downward/lower-right.
For the line $5x - 5y = 16$ (passes through $(16/5, 0)$ and $(0, -16/5)$ ):
- Inequality: $5x - 5y \le 16$
- Testing $(0,0)$ : $0 - 0 \le 16 \implies 0 \le 16$ (True).
- This means the region must be on the side containing the origin. Looking at this upper line, the origin is to its upper-left. So "towards the origin" means shading upward/upper-left.

Conclusion:

Graph 3 shades the region between the two lines.
Graph 1 shades the regions running outwards: below the lower line ( $x - y \ge 5$ ) and above the upper line ( $5x - 5y \le 16$ ).

2026: 18 May Shift 1

If the corner points of the bounded feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of the objective function $z = 2x+3y$ occurs at

2026: 15 May Shift 1

For the graph of a linear programming problem(LPP) given below. If $\min z = 3x+5y$ is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than $x, y \geq 0$ are

2026: 12 May Shift 2

The linear constraints for which the shaded region in the figure are:

2026: 21 May Shift 2

Consider an LPP:

Maximise $Z = 15x + 10y$

Subject to $2x + y \le 40$

$2x + 3y \le 80$

$x, y \ge 0$

Which of the following are correct?

A. The feasible region is bounded.

B. The corner points of the feasible region are $(0,0), (40,0), (10,20)$ and $(0,40)$ .

C. The corner points of the feasible region are $(0,0), (20,0), (10,20)$ and $\left(0, \dfrac{80}{3}\right)$ .

D. The maximum value of Z is 350.

Choose the correct answer from the options given below:

2026: 31 May Shift 2

If the corner points of the bounded feasible region for an LPP are $(5,0), (0,4), (0,2), (3,4)$ , and $(0,7)$ , then the minimum value of the objective function $z = 2x+5y$ occurs at :

2025: 14 May Shift 1

Which one of the following set of constraints does the given shaded region represent?

Which one of the following represents the correct feasible region determined by the following constraints x−y≥5x - y \geq 5x−y≥5, 5x−5y≤165x - 5y \leq 165x−5y≤16

Solution

Conclusion:

Related questions:

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CUET Mathematics Past Year Questions (Topic-Wise)

Which one of the following represents the correct feasible region determined by the following constraints

$x - y \geq 5$ , $5x - 5y \leq 16$