Algebra

Linear Programming

Easy

core

The feasible region associated with the inequality $2x + 3y > 4$ is

Open half plane containing the origin

Open half plane not containing the origin

Closed half plane containing the origin

Closed half plane not containing the origin

✅ Correct Option: 2

The inequality $2x + 3y > 4$ uses a strict inequality (>), not a non-strict inequality (≥).

A strict inequality represents an open half plane where the boundary line is not included.

This eliminates options with "closed" half plane.

To determine which side of the line the feasible region lies on, test the origin $(0, 0)$ .

Substitute $x = 0$ and $y = 0$ into $2x + 3y > 4$ :

$2(0) + 3(0) > 4$

$0 > 4$

This is false, so the origin does not satisfy the inequality.

The origin is not in the feasible region. Therefore, the feasible region is on the opposite side of the boundary line from the origin.

The feasible region is an open half plane not containing the origin.

2026: 29 May Shift 1

Let the corner points of the bounded feasible region of an LPP determined by a set of constraints are A(1, 5), B(3, 2) and C(2, 1). If the objective function $z=2ax+by$ , $a,b>0$ has maximum values at points A and B, and z has minimum value 8 at point C, then the value of $4a+b$ is:

2025: 14 May Shift 1

Which of the following is NOT a basic requirement of the linear programming problem (LPP)?

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Corner point of a feasible region	(I) The line segment joining any two arbitrary points of the region always lies entirely within the region
(B) Bounded feasible region	(II) can not be enclosed within a circle
(C) Unbounded feasible region	(III) can be enclosed within a circle
(D) Convex region	(IV) Is a point of intersection of two boundary lines in the feasible region

Choose the correct answer from the options given below:

2025: 16 May Shift 1

Consider the following L.P.P

Max. z = 5x + 2y; subject to -2x - 3y ≤ -6, x - 2y ≤ 2, 3x + 2y ≤ 12, -3x + 2y ≤ 3 and x, y ≥ 0 then

2026: 29 May Shift 1

The feasible region determined by the following constraints of a LPP

$x+y \ge 5$

$y \le 8$

$x \ge 0, y \ge 0$ is

2025: 14 May Shift 2

The maximum value of the objective function $Z = 2x + y$ of an LPP, subject to the constraints $x \leq 6, y \leq 2, x - y \leq 0$ , $x \geq 0, y \geq 0$ is

The feasible region associated with the inequality 2x+3y>42x + 3y > 42x+3y>4 is

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The feasible region associated with the inequality $2x + 3y > 4$ is