For the data given in table, the constraints are A x B y Maximum availability Number of labours 5 4 20 Work hours 6 3 12

5 x + 4 y ≤ 20 , 6 x + 3 y ≤ 12 , x ≥ 0 , y ≥ 0

5 x + 6 y ≤ 20 , 4 x + 3 y ≤ 12 , x ≥ 0 , y ≥ 0

5 x + 6 y ≥ 20 , 4 x + 3 y ≥ 20 , x ≥ 0 , y ≥ 0

5 x + 4 y ≥ 20 , 6 x + 3 y ≥ 12 , x ≥ 0 , y ≥ 0

Let p and q be the statements: p : 4 x + 5 y ≤ 20 , q : 3 x 2 + 2 y 2 ≤ 6

p but not q is a constraint of LPP

both p and q can be constraints of LPP

q but not p is a constraint of LPP

neither p nor q is a constraint of LPP

For the data given in the table, the constraints are Diet 1 x 1 Diet 2 x 2 Minimum requirement Proteins 2 15 30 Fats 12 6 48 Vitamins 5 10 20

2 x 1 + 15 x 2 ≥ 30 , 12 x 1 + 6 x 2 ≥ 48 , 5 x 1 + 10 x 2 ≥ 20 , x 1 ≥ 0 , x 2 ≥ 0

2 x 1 + 15 x 2 ≥ 30 , 12 x 1 + 6 x 2 ≥ 48 , 5 x 1 + 10 x 2 ≥ 20 , x 1 ≤ 0 , x 2 ≤ 0

2 x 1 + 15 x 2 ≤ 30 , 12 x 1 + 6 x 2 ≤ 48 , 5 x 1 + 10 x 2 ≤ 20 , x 1 ≤ 0 , x 2 ≤ 0

2 x 1 + 15 x 2 ≤ 30 , 12 x 1 + 6 x 2 ≤ 48 , 5 x 2 + 10 x 2 ≤ 20 , x 1 ≥ 0 , x 2 ≥ 0

MEDIUM

Earn 100

Define L.P.P and its advantages.

Important Questions on Models

EASY

Mathematics>Algebra>Models>Linear Programming

A printing company prints two types of magazines $A$ and $B$ . The company earns $₹ 10$ and $₹ 15$ on each magazine $A$ and $B$ , respectively. These are processed on three machines $I, I I$ and $I I I$ and total time in hours available per week on each machine is as follows:

	Magazine $A (x)$	Magazine $B (y)$	Time available
Machine $I$	$2$	$3$	$36$
Machine $I I$	$5$	$2$	$50$
Machine $I I I$	$2$	$6$	$60$

The number of constraints is

EASY

Mathematics>Algebra>Models>Linear Programming

For the data given in table, the constraints are

	$A (x)$	$B (y)$	Maximum availability
Number of labours	$5$	$4$	$20$
Work hours	$6$	$3$	$12$

EASY

Mathematics>Algebra>Models>Linear Programming

Priya has to stitch the tablecloth and curtains for a living. She has to put in

1

hour of work for a table cloth and

3

hours for a curtain. She gets

₹ 50

for every table cloth and

₹ 250

for every curtain. She has to earn at least

₹ 500

per day. Then, minimize the number of hours of work she has to put in every day.

EASY

Mathematics>Algebra>Models>Linear Programming

Which of the following cannot be considered as the objective function of a linear programming problem?

EASY

Mathematics>Algebra>Models>Linear Programming

Objective function of a linear programming problem is

EASY

Mathematics>Algebra>Models>Linear Programming

The corner points of the feasible region are

(800, 400), (1050, 150), (600, 0)

. The objective function is

P = 12 x + 6 y

. The maximum value of

P

MEDIUM

Mathematics>Algebra>Models>Linear Programming

Find the linear inequations for which the shaded area in the following figure is the solution set:

Question Image

EASY

Mathematics>Algebra>Models>Linear Programming

If the feasible region for a LPP is_____ (bounded/unbounded), then the optimal value of the objective function

Z = a x + b y

may or may not exist.

EASY

Mathematics>Algebra>Models>Linear Programming

The function to be maximized or minimized is called the

EASY

Mathematics>Algebra>Models>Linear Programming

The feasible solution of a

LLP

belongs to

EASY

Mathematics>Algebra>Models>Linear Programming

The corner points of the feasible region are

A (50, 50), B (10, 50), C (60, 0)

and

D (60, 40)

. The objective function is

P = \frac{5}{2} x + \frac{3}{2} y + 410 .

The minimum value of

P

is at point

EASY

Mathematics>Algebra>Models>Linear Programming

Let

p

and

q

be the statements:

p : 4 x + 5 y \leq 20, q : 3 x^{2} + 2 y^{2} \leq 6

EASY

Mathematics>Algebra>Models>Linear Programming

A wholesale merchant wants to start the business of cereal with

₹ 24000

. Wheat is

₹ 400

per quintal and rice is

₹ 600

per quintal. He has capacity to store

200

quintal of cereal. He earns profit of

₹ 25

per quintal on wheat and

₹ 40

per quintal on rice. If he stores

x

quintal rice and

y

quintal wheat, then for maximum profit the objective function is

EASY

Mathematics>Algebra>Models>Linear Programming

Shaded region is represented by

Question Image

MEDIUM

Mathematics>Algebra>Models>Linear Programming

For the data given in the table, the constraints are

	Diet $1 (x_{1})$	Diet $2 (x_{2})$	Minimum requirement
Proteins	$2$	$15$	$30$
Fats	$12$	$6$	$48$
Vitamins	$5$	$10$	$20$

EASY

Mathematics>Algebra>Models>Linear Programming

A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contain at least

8

units of vitamin

A

and

10

units of vitamin

C

. Food

I

contains

2

units per

kg

of vitamin

A

and

1

unit per

k g

of vitamin

C

, while food

II

contains

1

unit per

k g

of vitamin

A

and

2

units per

k g

of vitamin

C

. It costs

₹ 5

per

k g

to purchase food

I

and

₹ 7

per

k g

to purchase food

II

. Identify the objective function, so as to minimise the cost of mixture.

EASY

Mathematics>Algebra>Models>Linear Programming

A feasible region of a system of linear inequalities is said to be _____ if it can be enclosed within a circle.

EASY

Mathematics>Algebra>Models>Linear Programming

In a LPP, the linear inequalities or restrictions on the variables are called linear _____.

MEDIUM

Mathematics>Algebra>Models>Linear Programming

The value of an objective function is maximum under linear constraints

EASY

Mathematics>Algebra>Models>Linear Programming

The feasible region for a given $LPP$ is as shown in the figure. The $LPP$ has

Question Image

Define L.P.P and its advantages.

Important Questions on Models

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