Algebra

Linear Programming

Medium

core

The corner points of the feasible region with the constraints $x + y \leq 30$ , $x + y \geq 15$ , $y \leq 20$ , $x \leq 15$ and $x$ , $y \geq 0$ are

(0,0), (0, 15), (0,20), (15,0), (10, 20)

(0, 15), (20,0), (15,0), (10, 20)

(15,0), (15,15), (10, 20), (0, 20), (0,15)

(0, 0), (20,0), (0, 15), (15, 15)

✅ Correct Option: 3

The constraints are:

$x + y \leq 30$

$x + y \geq 15$

$y \leq 20$

$x \leq 15$

$x \geq 0$ and $y \geq 0$

The corner points occur where two boundary lines intersect. The boundaries are:

$x + y = 30$ , $x + y = 15$ , $y = 20$ , $x = 15$ , $x = 0$ , $y = 0$

Where $x = 0$ meets $x + y = 15$ :

$0 + y = 15$

$y = 15$

Point: $(0, 15)$

Where $x = 0$ meets $y = 20$ :

Point: $(0, 20)$

Where $y = 0$ meets $x + y = 15$ :

$x + 0 = 15$

$x = 15$

Point: $(15, 0)$

Where $x = 15$ meets $x + y = 30$ :

$15 + y = 30$

$y = 15$

Point: $(15, 15)$

Where $y = 20$ meets $x + y = 30$ :

$x + 20 = 30$

$x = 10$

Point: $(10, 20)$

The corner points of the feasible region are: $(15, 0)$ , $(15, 15)$ , $(10, 20)$ , $(0, 20)$ , $(0, 15)$

2026: 14 May Shift 2

In a linear programming problem, the corner points of the feasible region, determined by the system of linear inequalities are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z=5x+qy, q>0$ be the objective function. For what value of q the maximum value of z occurs at both (3, 4) and (0, 5)?

2025: 22 May Shift 1

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$ , $(0, 40)$ , $(20, 40)$ , $(60, 20)$ , $(60, 0)$ . If the objective function is $z = 4x + 3y$ , then which one of the following is true?

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

2023: 30 May Shift 3

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :

2026: 31 May Shift 2

Consider a LPP given by:

Maximize $z = 3x+4y$ ,

Subject to: $x+y \le 40$ , $x+2y \le 60$ , $x,y \ge 0$ .

Then which of the following statements are correct ?

A. The corner points of the feasible region are $(0,0), (0,30), (40,0), (20,20)$ .

B. The feasible region is unbounded.

C. The feasible region is bounded.

D. The maximum value of $z=3x+4y$ is obtained at $(60,40)$ .

Choose the correct answer from the options given below:

2025: 21 May Shift 2

The maximum value of $z = 5x + 7y$ subjected to constraints $x + y \leq 5$ , $x \geq 0$ , $y \geq 0$ is:

The corner points of the feasible region with the constraints x+y≤30x + y \leq 30x+y≤30, x+y≥15x + y \geq 15x+y≥15, y≤20y \leq 20y≤20, x≤15x \leq 15x≤15 and xxx, y≥0y \geq 0y≥0 are

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The corner points of the feasible region with the constraints $x + y \leq 30$ , $x + y \geq 15$ , $y \leq 20$ , $x \leq 15$ and $x$ , $y \geq 0$ are