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RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 12 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 30 - Linear programming.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 12 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 12 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming Page/Excercise 30.1

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RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming Page/Excercise 30.2

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Converting the inequations into equations, we obtain the lines

2x + 4y = 8, 3x + y = 6, x + y = 4, x = 0, y = 0.

These lines are drawn on a suitable scale and the feasible region of the LPP is shaded in the graph.

  

 

From the graph we can see the corner points as (0, 2) and (2, 0).

 

  

RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming Page/Excercise 30.3

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Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

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Note: Answer given in the book is incorrect.

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RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming Page/Excercise 30.4

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Solution 49

Let x and y units of commodity be transported from factory P to the depots at A and B respectively.

Then (8 - x - y) units will be transported to depot at C.

The flow is shown below.

 

  

 

  

 

  

Solution 50

   

 

  

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RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming Page/Excercise 30.5

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RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming Page/Excercise 30RE

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Corner points formed for:

Corner Points

Profit

Remarks

(0, 0)

Z = 100 × 0 + 120 × 0 = 0

 

(0, 10)

Z = 100 × 0 + 120 × 10 = 1200

 

(3, 8)

Z = 100 × 3 + 120 × 8 = 1260

Maximum

(17/3, 0)

Z = 100 × 17/3 + 120 × 0 = 1700/3

 

 

Revenue is maximum when x = 3, y = 8.

Maximum Profit = Rs. 1260

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Let us plot the constraints and find the feasible region through graph.

 

Thus the profit is maximum when the dealer buys 8 electronic sewing machines and 12 manual operated sewing machines.

 

Solution 19

Thus profit is maximum and is equal to Rs.1680

The company should manufacture 12 Type A machines and 6 Type B machines to maximize their profit.

 

RD Sharma Solution for Class 12 Science Mathematics Chapter 30 - Linear programming Page/Excercise MCQ

Solution 1

Correct option: (b)

  

Solution 2

Correct option: (b)

Objective function of a LPP is always maximized or minimized. Hence, it is optimized.

 

Solution 3

Correct option: (d)

Set of points between two parallel lines. Hence, set is connected. Set is convex.

Solution 4

Correct option: (b)

  

Solution 5

Correct option: (d)

  

From the graph we conclude that no feasible region exist.

 

Solution 6

Correct option: (c)

The maximum value of the objective function is attained at the points given by corner points of the feasible region.

Solution 7

Correct option: (d)

If we put x=0 and y=0 in all the equations then we get contradiction. Hence, region is on open half plane not containing origin. The region is unbounded we can not find the maximum value of the feasible region.

Solution 8

Correct option: (c)

  

 

Minimum Z will be at 2x + y 10. 

 

Solution 9

Correct option: (c)

  

  

 

Solution 10

Correct option: (a)

Optimization of objective function is depend on constraints. Hence, if the constraints in a linear programming problem are changed the problem is to be re-evaluated.

 

Solution 11

Correct option: (c)

Optimal solution of LPP has three types.

  1. Unique
  2. Infinite
  3. Does not exist.

Hence, it has infinite solution if it admits two optimal solution.

Solution 12

Correct option: (c)

As |x|=5 will only on x-axis. Hence, set is not connected to any two points between the set.

Hence, it is not convex.

Solution 13

Correct option: (b)

  

  

 

Solution 14

Correct option: (c)

As region is on origin side it is always bounded. Also, given that x,y 0 it is bounded in the first quadrant.

 

NOTE: Answer not matching with back answer.

Solution 15

Correct option: (d)

  

  

Solution 16

Correct option: (c)

To find maximum or minimum value of the region we use the coordinates of the vertices of feasible region. Hence, the value of objective function is maximum under linear constraints at any vertex of the feasible region.

 

Note: Answer not matching with back answer.

Solution 17

Correct option: (d)

Given that Z=px + qy

Maximum value at (3, 4) = maximum value at (0, 5)

3p+4q=5q

q=3p

 

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 30 - Linear programming for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 30 - Linear programming.

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CBSE XII Science - Mathematics

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