The region represented by the constraints x ≥ 0, y ≥ 0 of an LPP is Option 1: First quadrant Option 2: Second quadrant Option 3: Third quadrant Option 4: Fourth quadrant

Answer: First quadrant. Solution: The constraints are x ≥ 0 and y ≥ 0 for a Linear Programming Problem. The constraint x ≥ 0 means the x-coordinate is zero or positive (right side of the y-axis). The constraint y ≥ 0 means the y-coordinate is zero or positive (above the x-axis). The four quadrants of the coordinate plane:, Quadrant, x value, y value, Location, First (I), Positive (+), Positive (+), Top-right, Second (II), Negative (−), Positive (+), Top-left, Third (III), Negative (−), Negative (−), Bottom-left, Fourth (IV), Positive (+), Negative (−), Bottom-right, For the given constraints: x ≥ 0 → x is positive or zero y ≥ 0 → y is positive or zero Both x and y are non-negative, which corresponds to the First Quadrant. y-axis, II, I ← x ≥ 0, y ≥ 0, --------+-------- x-axis, III, IV, Therefore, the region represented by the constraints is the First Quadrant.

Algebra

Linear Programming

Easy

common

The region represented by the constraints $x \geq 0, y \geq 0$ of an LPP is

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

✅ Correct Option: 1

The constraints are $x \geq 0$ and $y \geq 0$ for a Linear Programming Problem.

The constraint $x \geq 0$ means the $x$ -coordinate is zero or positive (right side of the $y$ -axis).

The constraint $y \geq 0$ means the $y$ -coordinate is zero or positive (above the $x$ -axis).

The four quadrants of the coordinate plane:

Quadrant	x value	y value	Location
First (I)	Positive (+)	Positive (+)	Top-right
Second (II)	Negative (−)	Positive (+)	Top-left
Third (III)	Negative (−)	Negative (−)	Bottom-left
Fourth (IV)	Positive (+)	Negative (−)	Bottom-right

For the given constraints:

$x \geq 0$ → $x$ is positive or zero

$y \geq 0$ → $y$ is positive or zero

Both $x$ and $y$ are non-negative, which corresponds to the First Quadrant.

      y-axis
        |
   II   |   I  ← x ≥ 0, y ≥ 0
        |
--------+-------- x-axis
        |
   III  |   IV
        |

Therefore, the region represented by the constraints is the First Quadrant.

2023: 22 May Shift 3

Owner of a whole sale computers shop plans to sell 2 types of computers. A desktop and portable model. If $x$ is the number of desktops and $y$ is the number of portable model and the shop's capacity cannot exceed 250 units. Which of the following is correct ?

2026: 14 May Shift 2

The feasible region for a linear programming problem is shown in the figure.

Let $Z = 3x - 4y$ be the objective function, then minimum of Z occurs at the point

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: 30 May Shift 2

If the objective function for a LPP is $Z=3x+5y$ and the corner points of the bounded feasible region are (0, 0), (6, 0), (3, 5) and (0, 3), then the value of $|max(Z) - min(Z)|$ is:

2026: 25 May Shift 1

A company makes two types of cakes: type A and type B. it costs ₹ 360 to make a type A cake and ₹ 120 to make a type B cake. The company can make atmost 300 cakes and spend atmost ₹ 72,000 a day, the number of cakes of type B ( $y$ ) cannot exceed the number of type A ( $x$ ) cakes by more than 200.

The company makes a profit of ₹ 200 on each type A cake and ₹ 50 on each type B cake. A LPP to maximize the profit (₹) is

2022: 16 July Shift 2

The constraints are -

A. $2x + y \leq 8$

B. $2x + y \geq 8$

C. $x + 2y \leq 10$

D. $x + 2y \geq 10$

E. $x, y \geq 0$

Choose the correct answer from the options given below:

The region represented by the constraints x≥0,y≥0x \geq 0, y \geq 0x≥0,y≥0 of an LPP is

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The region represented by the constraints $x \geq 0, y \geq 0$ of an LPP is