For 0 ≤ p ≤ 1 and for any positive a , b ; let I ( p ) = ( a + b ) p , J ( p ) = a p + b p , then

I ( p ) < J ( p ) in 0 , p 2 and l ( p ) > J ( p ) in p 2 , ∞

I ( p ) < J ( p ) in p 2 , ∞ and J ( p ) < I ( p ) in 0 , p 2

Draw the graph of the inequality 3 x + 2 y ≤ 6 .

Given inequality is 3 x + 2 y ≤ 6 .....(i) Now, let us take equality equation 3 x + 2 y = 6 At x = 0 , y = 3 and y = 0 , x = 2 Now, put ( 0 , 0 ) in equation (i) ⇒ 0 ≤ 6 true Thus, solution region lies towards the origin.

Consider the linear programming problem: Maximize z = 10 x + 5 y subject to the constraints 2 x + 3 y ≤ 120 2 x + y ≤ 60 x , y ≥ 0 Then the coordinates of the corner points of the feasible region are

0 , 0 , 30 , 0 , 0 , 40 and 15 , 30

0 , 0 , 60 , 0 , 0 , 40 and 15 , 30

0 , 0 , 30 , 0 , 0 , 60 and 15 , 30

0 , 0 , 30 , 0 , 0 , 40 and 30 , 40

0 , 0 , 60 , 0 , 0 , 40 and 30 , 40

MEDIUM

Earn 100

Which of the following represents linear inequality in two variables?

79.17% studentsanswered this correctly

Important Questions on Linear Programming

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

For

0 \leq p \leq 1

and for any positive

a, b;

let

I (p) = (a + b)^{p}, J (p) = a^{p} + b^{p},

then

MEDIUM

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

Solve the following linear inequalities by graphical method:

$x + y \leq 4, x - y \leq 2, x \leq 2, x \geq 0, y \geq 0$ .,

HARD

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

Let

a, b, c, d, e

be real numbers such that

a + b < c + d, b + c < d + e, c + d < e + a, d + e < a + b .

Then

MEDIUM

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

The values of

x

for which

4^{x} + 4^{1 - x} - 5 < 0,

is given by

MEDIUM

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

The shaded region is the solution set of the inequalities

Question Image

HARD

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

β

satisfies the equation

x^{2} - x - 6 > 0

, then a value exists for

MEDIUM

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

5, 5 r, 5 r^{2}

are the lengths of the sides of a triangle, then

r

can not be equal to:

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

x^{2} - 5 x - 14 > 0 \Rightarrow x

lie outside

[α, β],

then

\frac{α}{β} =

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

Draw the graph of the inequality

3 x + 2 y \leq 6

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

Consider the linear programming problem:

Maximize $z = 10 x + 5 y$ subject to the constraints $2 x + 3 y \leq 120$

$2 x + y \leq 60$

$x, y \geq 0$

Then the coordinates of the corner points of the feasible region are

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

The cost and revenue functions of a product are given by

c (x) = 20 x + 4000

and

R (x) = 60 x + 2000

respectively where

x

is the number of items produced and sold. The value of

x

to earn profit is

MEDIUM

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

What is the area of the region enclosed by the inequalities

x \geq 0, y \geq 0, 4 x - y + 4 \leq 0

and

x - 3 y \geq 0 ?

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

The smallest negative integer satisfying both the quadratic inequalities

x^{2} < 4 x + 77

and

x^{2} > 4

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

The solution of the inequality

|x^{2} - 4 x| < 5

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

n \in N

then the statement

8 n + 16 \leq 2^{n}

is true for

MEDIUM

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

x^{2} + 6 x - 27 > 0

and

x^{2} - 3 x - 4 < 0

, then

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

x \in I

(set of all integers) such that

x^{2} - 3 x < 4

, then the number of possible values of

x

MEDIUM

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

Solve the inequality

4 x + 3 y > 12

by graphical method.

EASY

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

For the

LPP

; maximize

z = x + 4 y

subject to the constraints

x + 2 y \leq 2, x + 2 y \geq 8, x, y \geq 0

HARD

Mathematics>Algebra>Linear Programming>Linear Inequations in Two Variables

A system of linear equations in two variables,

p

and

q,

is given as

(n + 1) p + (n + 2) q = 8,

p - (n + 1) q + (n + 2) = 0, p + q = 3 .

Which of the following would be one of the values of

n

for which the given system of linear equations is consistent?

Which of the following represents linear inequality in two variables?

Important Questions on Linear Programming

Learn and Prepare for any exam you want !