For any linear programming problem the feasible region is shaded region as given below, then constraints are: Option 1: -2x+y ≥ 4, x+y ≥ 3, x-2y ≥ 2, x ≥ 0, y ≥ 0 Option 2: -2x+y ≤ 4, x+y ≥ 3, x-2y ≤ 2, x ≥ 0, y ≥ 0 Option 3: -2x+y ≤ 4, x+y ≤ 3, x-2y ≤ 2, x ≥ 0, y ≥ 0 Option 4: -2x+y ≥ 4, x+y ≤ 3, x-2y ≥ 2, x ≥ 0, y ≥ 0

Answer: -2x+y ≤ 4, x+y ≥ 3, x-2y ≤ 2, x ≥ 0, y ≥ 0. Solution: The shaded region lies away from the origin relative to x+y=3, so that constraint is x+y≥3. It lies on the origin side of both -2x+y=4 and x-2y=2, giving -2x+y≤4 and x-2y≤2. Together with x,y≥0 this matches the second option. Note: The shaded figure is not reproduced in this transcription; the inequality directions were fixed by the standard form of this region.

Algebra

Linear Programming

Medium

core

For any linear programming problem the feasible region is shaded region as given below, then constraints are:

$-2x+y \ge 4, x+y \ge 3, x-2y \ge 2, x \ge 0, y \ge 0$

$-2x+y \le 4, x+y \ge 3, x-2y \le 2, x \ge 0, y \ge 0$

$-2x+y \le 4, x+y \le 3, x-2y \le 2, x \ge 0, y \ge 0$

$-2x+y \ge 4, x+y \le 3, x-2y \ge 2, x \ge 0, y \ge 0$

✅ Correct Option: 2

The shaded region lies away from the origin relative to $x+y=3$ , so that constraint is $x+y\ge3$ .

It lies on the origin side of both $-2x+y=4$ and $x-2y=2$ , giving $-2x+y\le4$ and $x-2y\le2$ .

Together with $x,y\ge0$ this matches the second option.

Note: The shaded figure is not reproduced in this transcription; the inequality directions were fixed by the standard form of this region.

2026: 22 May Shift 2

Consider the LPP: Minimize $z=-50x+20y$ subject to $2x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0$ . Then which of the following statements are TRUE?

(A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0).

(B) The optimum value of the objective function is -300

(D) The optimum value of the objective function is 100

Choose the correct answer from the options given below:

2025: 13 May Shift 1

Consider the LPP: Maximize $z = x + y$ subject to the constraints $x + 2y \leq 70$ , $2x + y \leq 95$ , $x,y \geq 0$ . The optimal feasible solution is

2022: 25 May Shift 1

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :

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

2025: 26 May Shift 2

For the objective function Z=-4x + 6y subject to the constraints 3x + 2y ≥ 5, 7x + 2y ≤ 9, x ≥ 0, y ≥ 0, the maximum value of Z occurs at $(a, b)$ and the minimum value of Z occurs at $(p, q)$ then the value of $\frac{a}{p} + \frac{b}{q}$ is:

2025: 16 May Shift 1

Consider the following L.L.P.

Minimize z = 30x - 30y + 1800;

subject to x + y ≤ 30, x ≤ 15, y ≤ 20, x + y ≥ 15 and x, y ≥ 0.

Then it attains its optimal value at the point

For any linear programming problem the feasible region is shaded region as given below, then constraints are:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)