Algebra

Linear Programming

Medium

core

In a linear programming problem, the constraints on decision variables $x$ and $y$ are $y-2x \leq 0$ , $y \geq 0$ , $0 \leq x \leq 5$ . The feasible region of the above problem:

is bounded in the first quadrant

is unbounded in the first quadrant

is unbounded in first and second quadrants

does not exist

✅ Correct Option: 1

We need to find the feasible region defined by these constraints:

$y - 2x \leq 0 \implies y \leq 2x$

$y \geq 0$

$0 \leq x \leq 5$

$y \leq 2x$ means the region below (or on) the line $y = 2x$ , which passes through the origin with slope $2$ .

$y \geq 0$ means we stay on or above the $x$ -axis.

$0 \leq x \leq 5$ means we stay between the $y$ -axis and the vertical line $x = 5$ .

The region where all constraints overlap is bounded by three corner points, found by intersecting the boundary lines:

At $x = 0$ and $y = 0$ :

$A = (0,\, 0)$

At $x = 5$ and $y = 0$ :

$B = (5,\, 0)$

At $x = 5$ and $y = 2x$ :

$y = 2(5) = 10$

$C = (5,\, 10)$

Connecting $(0,\, 0)$ , $(5,\, 0)$ , and $(5,\, 10)$ gives us a triangle with:

Base along the $x$ -axis $= 5$

Vertical side from $(5,\, 0)$ to $(5,\, 10)$ $= 10$

The feasible region is a triangle with vertices at $(0,\, 0)$ , $(5,\, 0)$ , and $(5,\, 10)$ .

2025: 14 May Shift 1

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

2026: 22 May Shift 1

The corner points of the bounded feasible region determined by $x+3y\le60, x+y\ge10, x\le y, x\ge0, y\ge0$ are A(0, 10), B(5, 5), C(15, 15) and D(0, 20). If the objective function $z=ax+by$ has its maximum value on the line segment CD, then the relation between $a$ and $b$ is:

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The solution set of the linear constraints $x - 2y \geq 0, 2x - y \leq -4, x \geq 0$ and $y \geq 0$ is

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If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$ , $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$ , when $z$ is maximum at $D(4,10)$ and $C(6,8)$ , is:

2026: 31 May Shift 2

A LPP $max\,z = ax+by$ having bounded feasible region with vertices on $(2,1), (3,2), (5,6)$ and $(1,7)$ . Then which of following are TRUE?

A. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = 4a$

B. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = -4a$

C. $max\,z$ does not exist

D. if $max\,z$ occurs at $(1,7)$ and $(5,6)$ , then $max\,z$ occurs for infinite number of value of $x$ and $y$

Choose the correct answer from the options given below:

2026: 22 May Shift 1

If the objective function for a LPP is $Z=3x+4y$ and the corner points for bounded feasible region are (9,0), (4,3), (2,5) and (0,8), then the maximum value of Z occurs at

In a linear programming problem, the constraints on decision variables xxx and yyy are y−2x≤0y-2x \leq 0y−2x≤0, y≥0y \geq 0y≥0, 0≤x≤50 \leq x \leq 50≤x≤5. The feasible region of the above problem:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

In a linear programming problem, the constraints on decision variables $x$ and $y$ are $y-2x \leq 0$ , $y \geq 0$ , $0 \leq x \leq 5$ . The feasible region of the above problem: