RD Sharma Class 12 Exercise 29.3 Linnear Programing Solutions Maths - Download PDF Free Online

# RD Sharma Class 12 Exercise 29.3 Linnear Programing Solutions Maths - Download PDF Free Online

Edited By Lovekush kumar saini | Updated on Jan 25, 2022 02:52 PM IST

Maths for Class 12 students requires a lot of practice and efficiency. To ensure proper preparation, students need to practice from materials that are detailed and cover all concepts. RD Sharma materials are the best books for CBSE maths as they are comprehensive and contain questions from all concepts.

RD Sharma Class 12th Exercise 29.3 covers the chapter Linear Programming that contains a total of 15 sums that are of Level 1 difficulty. This exercise contains different conditions in which students have to calculate the minimum of values using linear programming. While constructing and solving linear programming problems, some of the important terms which we shall be using here. RD Sharma solutions They are Objective function, feasible region, Optimization problem, Optimal solution.

## Linear Programming Excercise: 29.3

Linear Programming Exercise 29.3 Question 5

Hint: Draw a graph
Given: 1 Kg of Food X costs ? 5, 1Kg of Food Y costs ? 8.
Solution: We need to minimize
$z =5x + 5y$
sub to contraits
$\Rightarrow x+2y\geq 6$ ...(i)
$\Rightarrow x+y\geq 7$ ...(ii)
$\Rightarrow x+3y\geq 11$ ....(iii)
$\Rightarrow 2x+y\geq 9$ ...(iv)

Solving (ii) & (iii)
$x=2,y=5$
Solving (ii) & (iv)
$x=5,y=2$
 Points Value of z (2,5) 50 (5,2) 41 (0,9) 72 (11.0) 55
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The minimum cost is ? 41

Linear Programming Exercise 29 .3 Question 6

Hint: Draw the graph and find plane
Given: 1 unit of F1 contain 4 unit and F2 contain 6 unit of mineral.
Solution: Let ‘x’ units of $F_{1}$ and ‘y’ unit of F2 in the food.
Minimum $z=4x+6y$ ......(i)
$3x+6y\geq 30$ ......(ii)
$4x+3y\geq 100$......(iii)
$x\geq 0,y\geq 0$ ......(iv)
Solving (i) & (ii)
$x=24,y=4/3$
 Points Value of z $\left ( 80/3,0 \right )$ $320/3$ $\left ( 24,4/3 \right )$ $104$ $\left ( 0,100/3 \right )$ $200$

Minimum cost: 104

Linear Programming Exercise 29.3 Question 8

Hint: Draw a graph
Given: Mixture A costs ? 8 per Kg and B costs ?12 per Kg
Solution: Let ‘x’ be the quantity of A mixture and ‘y’ be the quantity of B mixture
Minimize,
$8x + 12y =z$
sub to contraits
$\begin{gathered} 60 x+30 y \geq 240 \Rightarrow 2 x+y \geq 8 \\ \end{gathered}$
$\begin{gathered} 30 x+60 y \geq 300 \Rightarrow x+2 y \geq 10 \\ \end{gathered}$
$\begin{gathered} 30 x+180 y \geq 540 \Rightarrow x+6 y \geq 18 \\ \end{gathered}$
$\begin{gathered} x \geq 0, y \geq 0 \end{gathered}$
Solving (i) & (ii), we get
$x=2,y=4$
Solving (ii) & (iii) we get
$x=6,y=2$
 Points Value of z $\left ( 0,8 \right )$ $6$ $\left ( 2,4 \right )$ $72$ $\left ( 6,2 \right )$ $72$ $\left ( 18,0 \right )$ $144$

Minimum cost is ? 72.

Linear Programming Exercise 29.3 Question 14

Hint: Draw the graph
Given: 1 Kg of X costs ? 16 and 1Kg of Y costs ? 20.
Solution: Let ‘x’ unit of Food X and ‘y’ unit of Food Y
Minimum $Z = 16x + 20y$
sub to,
\begin{aligned} &x+2 y \geq 10 \\ \end{aligned} ...(i)
\begin{aligned} &2 x+2 y \geq 12 \\ \end{aligned}
\begin{aligned} &\Rightarrow x+y \geq 6 \\ \end{aligned} ...(ii)
\begin{aligned} &3 x+y \geq 8 \end{aligned} .....(iii)
Solving (ii) & (iii),
$x=1,y=5$
 Point Value of z $\left ( 0,8 \right )$ 160 $\left ( 2,4 \right )$ 110 $\left ( 1,5 \right )$ 116 $\left ( 10,0 \right )$ 160

Minimum cost = 160

Also, see

RD Sharma Solutions Class 12 Mathematics Chapter 29 Exercises 29.1

RD Sharma Solutions Class 12 Mathematics Chapter 29 Exercises 29.2

RD Sharma Solutions Class 12 Mathematics Chapter 29 Exercises 29.4

RD Sharma Solutions Class 12 Mathematics Chapter 29 Exercises 29.5

RD Sharma Solutions Class 12 Mathematics Chapter 29 MCQ

RD Sharma Solutions Class 12 Mathematics Chapter 29 FBQ

RD Sharma Class 12th Exercise 29.3 material contains solved questions from the RD Sharma book. It is the best alternative for exam preparation as it complies with the CBSE syllabus and covers the entire syllabus. Some of the benefits of this material are:

1. Designed by experts

RD Sharma Class 12th Exercise 29.3 solutions are prepared by a group of subject experts with years of experience with CBSE question paper patterns. Every answer from this material goes through a series of quality checks to ensure that the steps are accurate and the information provided is of the best quality.

2. Exam-oriented material

As RD Sharma books are widely used, there is a possibility that questions from this material might appear in the exams. This is why students should practice RD Sharma Class 12th Exercise 29.3 material regularly to get a better understanding of the chapter. Moreover, as class 12 students have to write their entrance exams in the future, this material can be helpful for their preparation.

3. Ease of use

RD Sharma Class 12th Exercise 29.3 material is available on career 360's website, which the students can access using any device with an internet connection. They have to search the chapter name and exercise number to get relevant results on the website. This means that students can access it from anywhere, anytime.

4. Easy for quick reference

If students find it hard to study from the RD Sharma book, they can refer to RD Sharma Class 12 Chapter 29 Exercise 29.3 material as it covers the entire syllabus. It contains step-by-step solutions which are easy to understand and revise. Instead of searching the whole RD Sharma textbook, students can quickly revise this material to save time.

5. Free of cost

Career360 has prepared Class 12 RD Sharma Chapter 29 Exercise 29.3 Solutions to help students overcome issues with their exam preparation. This is why the entire material is provided on their website for free. Students can take advantage of this material to finish the syllabus and stay ahead of their class.

## RD Sharma Chapter wise Solutions

1. Where can I find solutions to RD Sharma's class 12 maths chapters?

You can find solutions to all the chapters and Career360's website. In addition, students can search the chapter name and exercise number on the website to get their material.

2. Is the entire material available free of cost?

Yes, Career360 provides the entire RD Sharma Class 12 Solutions Linear Programming Ex 29.3 material free of cost to help students prepare for their exams.

3. Can I solve NCERT questions after preparing this material?

RD Sharma and NCERT books follow a similar concept which is why students can quickly solve NCERT questions once they are done with this material.

4. Can I access this material through my phone?

Yes, RD Sharma Class 12 solutions Chapter 29 Ex 29.3 can be accessed through any device, internet connection, and browser. Students can study from their phones, laptops, tablets, etc.

5. What are the applications of linear programming?

Some of the applications of linear programming are:

• Factories and production houses

• Energy industry

• Agricultural sector

• Large-scale manufacturing, etc.

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