The shaded unbounded area of an LPP is the result of constraints: Option 1: x ≥ 8, y-x ≥ 5; x,y ≥ 0 Option 2: x ≤ 8, y-x ≤ 5; x,y ≥ 0 Option 3: x ≥ 8, y-x ≤ 5; x,y ≥ 0 Option 4: x ≤ 8, y-x ≥ 5; x,y ≥ 0

Answer: x ≤ 8, y-x ≥ 5; x,y ≥ 0. Solution: The region lies to the left of the vertical line x = 8 and above the line y = x + 5, which is unbounded upwards. This corresponds to x ≤ 8 and y - x ≥ 5 with x, y ≥ 0. Note: The accompanying graph is not reproduced here, so the shading has been inferred from the option that yields an unbounded region consistent with the given boundary lines.

Algebra

Linear Programming

Medium

applied

The shaded unbounded area of an LPP is the result of constraints:

$x \ge 8, y-x \ge 5; x,y \ge 0$

$x \le 8, y-x \le 5; x,y \ge 0$

$x \ge 8, y-x \le 5; x,y \ge 0$

$x \le 8, y-x \ge 5; x,y \ge 0$

✅ Correct Option: 4

The region lies to the left of the vertical line $x = 8$ and above the line $y = x + 5$ , which is unbounded upwards. This corresponds to $x \le 8$ and $y - x \ge 5$ with $x, y \ge 0$ .

Note: The accompanying graph is not reproduced here, so the shading has been inferred from the option that yields an unbounded region consistent with the given boundary lines.

2022: 25 May Shift 1

The programming problem

Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

2025: 21 May Shift 2

Which of the region shown in the given figures represents the feasible region bounded by the following constraints?

$4x + y \geq 80$ , $2x + y \geq 60$ , $x + y \leq 80$ , $x \geq 0$ , $y \geq 0$

2022: 7 Aug Shift 2

The solution of LPP

max.(z) = $5x + 3y$ subject to

$2x + y \leq 6$

$x + y \leq 4$

$x \geq 0, y \geq 0$ , is

2026: 26 May Shift 2

Consider an LPP:

Maximize $Z = 5x + y$

Subject to $x + 3y \le 12$

$3x + y \le 12$

and $x,y \ge 0$

then which of the following statements are TRUE ?

A. The corner points of the bounded feasible region are (0,0), (4,0), (3,3) and (0,4).

B. Maximum value of $z$ occurs at (3,3).

C. Maximum value of $z$ occurs at (4,0).

D. The maximum value of $z$ is 20.

Choose the correct answer from the options given below:

2025: 30 May Shift 2

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

2025: 14 May Shift 1

The corner points of the feasible region associated with the LPP: Maximise $Z = px + qy$ , $p,q > 0$ subject to $2x + y \leq 10$ , $x + 3y \leq 15$ , $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

The shaded unbounded area of an LPP is the result of constraints:

Solution

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