CUET Mathematics - Algebra - Linear Programming | Free Questions - Page 9

Q1:

2022: 30 Aug Shift 1

Algebra

>

Linear Programming

Medium

Core

The corner points of the feasible region for an L.P.P. are $(0, 10)$ , $(5, 5)$ , $(15, 15)$ and $(0, 20)$ . If the objective function is $z = px + qy$ ; $p, q > 0$ , then the condition on $p$ and $q$ so that the maximum of $z$ occurs at $(15, 15)$ and $(0, 20)$ is

$p = q$

$p = 2q$

$q = 3p$

$q = 2p$

Correct Answer

Option 3

Correct Answer

Explanation

Q2:

2022: 16 July Shift 2

Algebra

>

Linear Programming

Easy

Core

Case Study

A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 unit/kg of vitamin A and 1 unit/kg of vitamin C. Food 'II' contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin C. It cost Rs.50 per kg to purchase Food 'I' and Rs 70 per kg to purchase Food 'II'

Let x kg of food 'I' and y kg of food 'II' be mixed together for daily vitamin requirement in the family at minimum cost. Based on this information answer the question:

Objective function of LPP is:

$z = 50x + 70y$

$z = 2x + y$

$z = x + 2y$

$z = 70x + 50y$

Correct Answer

Option 1

Correct Answer

Explanation

Q3:

2022: 16 July Shift 2

Algebra

>

Linear Programming

Easy

Core

Case Study

A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 unit/kg of vitamin A and 1 unit/kg of vitamin C. Food 'II' contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin C. It cost Rs.50 per kg to purchase Food 'I' and Rs 70 per kg to purchase Food 'II'

Let x kg of food 'I' and y kg of food 'II' be mixed together for daily vitamin requirement in the family at minimum cost. Based on this information answer the question:

The constraints are -

A. $2x + y \leq 8$

B. $2x + y \geq 8$

C. $x + 2y \leq 10$

D. $x + 2y \geq 10$

E. $x, y \geq 0$

Choose the correct answer from the options given below:

A, C, E only

B, C, E only

B, D, E only

A, D, E only

Correct Answer

Option 3

Correct Answer

Explanation

Q4:

2022: 16 July Shift 2

Algebra

>

Linear Programming

Medium

Core

Case Study

A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 unit/kg of vitamin A and 1 unit/kg of vitamin C. Food 'II' contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin C. It cost Rs.50 per kg to purchase Food 'I' and Rs 70 per kg to purchase Food 'II'

Let x kg of food 'I' and y kg of food 'II' be mixed together for daily vitamin requirement in the family at minimum cost. Based on this information answer the question:

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:

A and C only

A and D only

B and D only

B and E only

Correct Answer

Option 4

Correct Answer

Explanation

Q5:

2022: 16 July Shift 2

Algebra

>

Linear Programming

Easy

Core

Case Study

A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 unit/kg of vitamin A and 1 unit/kg of vitamin C. Food 'II' contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin C. It cost Rs.50 per kg to purchase Food 'I' and Rs 70 per kg to purchase Food 'II'

Let x kg of food 'I' and y kg of food 'II' be mixed together for daily vitamin requirement in the family at minimum cost. Based on this information answer the question:

The feasible solution to the LPP is-

$x = 2, y = 4$

$x = 4, y = 2$

Does not exist

$x = 4, y = 0$

Correct Answer

Option 1

Correct Answer

Explanation

Q6:

2022: 16 July Shift 2

Algebra

>

Linear Programming

Easy

Core

Case Study

A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 unit/kg of vitamin A and 1 unit/kg of vitamin C. Food 'II' contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin C. It cost Rs.50 per kg to purchase Food 'I' and Rs 70 per kg to purchase Food 'II'

Let x kg of food 'I' and y kg of food 'II' be mixed together for daily vitamin requirement in the family at minimum cost. Based on this information answer the question:

The minimum cost of the mixture is-

Rs 560

Rs 380

Rs 320

Rs 500

Correct Answer

Option 2

Correct Answer

Explanation

Q7:

2022: 23 Aug Shift 1

Algebra

>

Linear Programming

Easy

Core

If the objective function for an LPP is max. $(z) = 300x + 700y$ and the corner points for the bounded feasible region are $(6,0)$ $(5,0)$ $(0,6)$ $(4,4)$ and $(0,4)$ , then the maximum values of z occurs at :

$(0, 6)$

$(4, 4)$

$(6, 0)$

$(0, 4)$

Correct Answer

Option 1

Correct Answer

Explanation

Q8:

2022: 23 Aug Shift 1

Algebra

>

Linear Programming

Medium

Core

The feasible region and optimal solution of a LPP with objective function, max. $(z) = 600x + 400y$ , subject to :

$x + 2y \leq 12$ , $2x + y \leq 12$ , $x + 1.25y \geq 5$ , $x \geq 0$ and $y \geq 0$ , is:

The feasible region and optimal solution is _____

BCGB and optimal solution occurs at $(12, 0)$

ABCDEA and optimal solution occurs at $(4, 4)$

ABCDEA and optimal solution occurs at $(0, 6)$

FDCF and optimal solution occurs at $(0, 12)$

Correct Answer

Option 2

Correct Answer

Explanation

Q9:

2022: 25 May Shift 1

Algebra

>

Linear Programming

Easy

Common

The programming problem

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

not an LPP

an LPP, with unbounded feasible region and no solution

an LPP, and Max $Z = 18$ , at $x = 3, y = 4$

an LPP, and Max $Z = 12$ , at $x = 0, y = 4$

Correct Answer

Option 3

Correct Answer

Explanation

Q10:

2022: 25 May Shift 1

Algebra

>

Linear Programming

Easy

Common

The solution of a LPP with basic feasible solutions (0, 0), (10, 0), (0, 20), (10, 15) and objective function Max $Z = 2x + 3y$ is :

$x = 0, y = 20$ , Max $Z = 60$

$x = 10, y = 15$ , Max $Z = 65$

$x = 10, y = 20$ , Max $Z = 70$

$x = 15, y = 10$ , Max $Z = 60$

Correct Answer

Option 2

Correct Answer

Explanation

Q11:

2022: 25 May Shift 1

Algebra

>

Linear Programming

Medium

Core

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :

$x + y \geq 50$

$2x + y \leq 80$

$x, y \geq 0$

$x + y \leq 50$

$2x + y \geq 80$

$x, y \geq 0$

$x + y \leq 50$

$2x + y \leq 80$

$x, y \geq 0$

$x + y \geq 50$

$2x + y \geq 80$

$x, y \geq 0$

Correct Answer

Option 3

Correct Answer

Explanation

Q12:

2022: 25 May Shift 1

Algebra

>

Linear Programming

Medium

Core

The feasible region of an LPP Max $Z = 3x + 2y$ subject to $x \geq 0, y \geq 0, x - 2y \leq 3$ is:

Bounded in first quadrant but has no solution

Unbounded in first quadrant but has a solution

Unbounded in first quadrant and has no solution

Bounded and has a solution $x = 0, y = 0, Z = 0$

Correct Answer

Option 3

Correct Answer

Explanation

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