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# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 - Linear Programming Problems [Latest edition]

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#### Chapters ## Chapter 2: Linear Programming Problems

MCQShort Answers ILong Answers II
MCQ

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Linear Programming Problems MCQ

#### 2 marks each

MCQ | Q 1

The corner points of the feasible solutions are (0, 0) (3, 0) (2, 1) (0, 7/3) the maximum value of Z = 4x + 5y is

• 12

• 13

• 35/3

• 0

MCQ | Q 2

The half plane represented by 4x + 3y >14 contains the point

• (0, 0)

• (2, 2)

• (3, 4)

• (1, 1)

MCQ | Q 3

The feasible region is the set of point which satisfy.

• The object functions

• All the given constraints

• Some of the given constraints

• Only one constraint

MCQ | Q 4

Choose the correct alternative:

Objective function of LPP is

• A constraint

• A function to be maximized or minimized

• A relation between the decision variables

• A feasible region

• Equation of straight line

MCQ | Q 5

The value of objective function is maximum under linear constraints

• At the center of the feasible region

• At (0, 0)

• At vertex of feasible region

• At (−1, −1)

MCQ | Q 6

If a corner point of the feasible solutions are (0, 10) (2, 2) (4, 0) (3, 2) then the point of minimum Z = 3x + 2y is

• (2, 2)

• (0, 10)

• (4, 0)

• (3, 2)

MCQ | Q 7

The point of which the maximum value of z = x + y subject to constraints x + 2y ≤ 70, 2x + y ≤ 90, x ≥ 0, y ≥ 0 is obtained at

• (30, 25)

• (20, 35)

• (35, 20)

• (40, 15)

MCQ | Q 8

A solution set of the inequality x ≥ 0

• Half plane on the Left of y-axis

• Half plane on the right of y axis excluding the point on y-axis

• Half plane on the right of y-axis including the point on y-axis

• Half plane on the upword of x-axis

MCQ | Q 9

Which value of x is in the solution set of inequality − 2X + Y ≥ 17

• − 8

• − 6

• − 4

• 12

MCQ | Q 10

The graph of the inequality 3X − 4Y ≤ 12, X ≤ 1, X ≥ 0, Y ≥ 0 lies in fully in

• I quadrant

• II quadrant

• III quadrant

• IV quadrant

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Short Answers I

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Linear Programming Problems Short Answers I

#### 2 marks

Short Answers I | Q 1

Solve each of the following inequations graphically using XY-plane:

4x - 18 ≥ 0

Short Answers I | Q 2

Sketch the graph of inequation x ≥ 5y in xoy co-ordinate system

Short Answers I | Q 3

Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1

Short Answers I | Q 4

Find the feasible solution of linear inequation 2x + 3y ≤ 12, 2x + y ≤ 8, x ≥ 0, y ≥ 0 by graphically

Short Answers I | Q 5

Solve graphically: x ≥ 0 and y ≥ 0

Short Answers I | Q 6

Find the solution set of inequalities 0 ≤ x ≤ 5, 0 ≤ 2y ≤ 7

Short Answers I | Q 7

Find the feasible solution of the following inequation:

3x + 2y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0

Short Answers I | Q 8

Draw the graph of inequalities x ≤ 6, y −2 ≤ 0, x ≥ 0, y ≥ 0 and indicate the feasible region

Short Answers I | Q 9

Check the ordered points (1, −1), (2, −1) is a solution of 2x + 3y − 6 ≤ 0

Short Answers I | Q 10

Show the solution set of inequations 4x – 5y ≤ 20 graphically

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Long Answers II

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Linear Programming Problems Long Answers II

#### 4 Marks

Long Answers II | Q 1

Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0

Long Answers II | Q 2

Maximize z = 7x + 11y subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0

Long Answers II | Q 3

Maximize z = 10x + 25y subject to x + y ≤ 5, 0 ≤ x ≤ 3, 0 ≤ y ≤ 3

Long Answers II | Q 4

Maximize z = 3x + 5y subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0 also find the maximum value of z

Long Answers II | Q 5

Minimize Z = 8x + 10y subject to 2x + y ≥ 7, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0

Long Answers II | Q 6

Minimize z = 7x + y subjected to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0

Long Answers II | Q 7

Minimize z = 6x + 21y subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points

Long Answers II | Q 8

Minimize z = 2x + 4y is subjected to 2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points

Long Answers II | Q 9

Maximize z = −x + 2y subjected to constraints x + y ≥ 5, x ≥ 3, x + 2y ≤ 6, y ≥ 0 is this LPP solvable? Justify your answer

Long Answers II | Q 10

x − y ≤ 1, x − y ≥ 0, x ≥ 0, y ≥ 0 are the constant for the objective function z = x + y. It is solvable for finding optimum value of z? Justify?

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## Chapter 2: Linear Programming Problems

MCQShort Answers ILong Answers II ## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 - Linear Programming Problems

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 (Linear Programming Problems) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 Linear Programming Problems are Linear Inequations in Two Variables, Linear Programming Problem (L.P.P.), Lines of Regression of X on Y and Y on X Or Equation of Line of Regression, Graphical Method of Solving Linear Programming Problems, Linear Programming Problem in Management Mathematics.

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