The linear constraints for which the shaded region in the figure are: Option 1: x+3y≤60, x≤ y, x+y≤10, x≥0, y≥0 Option 2: x+3y≤60, x≥ y, x+y≥10, x≥0, y≥0 Option 3: x+3y≤60, x≤ y, x+y≥10, x≥0, y≥0 Option 4: x+3y≥60, x≥ y, x+y≥10, x≥0, y≥0

Answer: x+3y≤60, x≤ y, x+y≥10, x≥0, y≥0. Solution: The shaded region lies below the line x+3y=60, above the line x+y=10, and on the side of y=x where y≥ x, together with x≥0 and y≥0. Its corners are (0,10), (5,5), (15,15) and (0,20). Note: The figure is not reproduced with the text; we identified the set whose half-planes generate this standard shaded region.

Algebra

Linear Programming

Medium

core

The linear constraints for which the shaded region in the figure are:

$x+3y\le60, x\le y, x+y\le10, x\ge0, y\ge0$

$x+3y\le60, x\ge y, x+y\ge10, x\ge0, y\ge0$

$x+3y\le60, x\le y, x+y\ge10, x\ge0, y\ge0$

$x+3y\ge60, x\ge y, x+y\ge10, x\ge0, y\ge0$

✅ Correct Option: 3

The shaded region lies below the line $x+3y=60$ , above the line $x+y=10$ , and on the side of $y=x$ where $y\ge x$ , together with $x\ge0$ and $y\ge0$ . Its corners are $(0,10)$ , $(5,5)$ , $(15,15)$ and $(0,20)$ .

Note: The figure is not reproduced with the text; we identified the set whose half-planes generate this standard shaded region.

2022: 30 Aug Shift 1

In linear programming, the optimal value of the objective function is attained at the points given by

2022: 16 July Shift 2

The type of feasible region and its corner points are.

A. bounded

B. unbounded

C. (0,5), (2,4), (10,0)

D. (0,8), (2,4), (4,0)

E. (0,8), (2,4), (10,0)

Choose the correct answer from the options given below:

2023: 30 May Shift 3

The corner points of the feasible region determined by the following system of linear inequalities :

$2x + y \leq 10$ , $x + 3y \leq 15$ , $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px + qy$ , where $p, q > 0$ condition on p and q so that maximum of z occurs at both (3, 4) and (0, 5) is :

2026: 30 May Shift 1

For a LPP, the objective function is $z=4x+3y$ and the feasible region determined by a set of linear constraints is shown in the graph as a shaded portion. Which one of the following statement is true ?

2025: 3 June Shift 2

The point which provides the optimal solution of the linear programming problem

maximize $z = 21x + 35y$

$3x + 2y \leq 30$

$4x + 5y \leq 60$

$x \geq 0, y \geq 0$

has the coordinates

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:

The linear constraints for which the shaded region in the figure are:

Solution

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