RD Sharma Class 12 Exercise 29.3 Linnear Programing Solutions Maths

Lovekush kumar sainiUpdated on 25 Jan 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.

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RD Sharma Class 12 Solutions Chapter29Linear Programming - Other Exercise
Linear Programming Excercise: 29.3
RD Sharma Chapter wise Solutions

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.

RD Sharma Class 12 Solutions Chapter29Linear Programming - Other Exercise

Linear Programming Excercise: 29.3

Linear Programming Exercise 29.3 Question 5

Answer: 41
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

Answer: 104
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

Answer: ?72
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

Answer: 440
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:

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2. Exam-oriented material

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