RD Sharma Class 12 Exercise FBQ Linnear Programing Solutions Maths

Lovekush kumar sainiUpdated on 25 Jan 2022, 02:51 PM IST

RD Sharma books are considered to be the benchmark of maths textbooks. This is because they have a strong reputation for being highly informative and detailed. This is why many schools follow RD Sharma textbooks to set up the question papers and for class lectures. In addition, RD Sharma class 12th exercise FBQ material is explicitly designed for students who want to get more insight on the subject and score good marks in exams.

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RD Sharma Class 12 Solutions Chapter29 FBQ Linear Programming - Other Exercise
Linear Programming Excercise: 29 FBQ
RD Sharma Chapter wise Solutions

RD Sharma class 12 chapter 29 exercise FBQ material consists of 15 fill-in-the-blank questions based on fundamentals. RD Sharma solutions Linear Programming FBQ cover topics like LPP, finding optimal solution coordinates, maximum value, linear inequalities, etc.

RD Sharma Class 12 Solutions Chapter29 FBQ Linear Programming - Other Exercise

Linear Programming Excercise: 29 FBQ

Linear Programming exercise Fill in the blanks question 1

Answer:

In a LPP, the objective function is always linear.
Hint:
For this type of question, we should know about the properties of linear programing, objective function and objective constraints.
Given:
In a LPP, the objective function is always ____
Solution:
We have given any linear programming and we have to tell, if the objective function and objective constraints are solve or linear or quadratic or adjacent
There are some properties present in a linear programming problems like any linear programming problems must have the relationship between variables and constraints must be linear.
The constants must be non-negative that it is always a positive value.
So, In a LPP, the objective function is always linear.

Linear Programming exercise Fill in the blanks question 2

Answer:

The feasible region for an LPP is always a convex polygon

Hint:

We have to be known the properties of polygon

Given:

The feasible region for an LPP is always a ______ polygon.

Solution:

In a convex polygon, all the interiors are $< 180^{\circ}$

In a concave polygon, in which at least one angle is more than $180^{\circ}$

So, the feasible region for an LPP is always a convex polygon.

Linear Programming exercise Fill in the blanks question 5

Answer:

A corner point of a feasible region is a point in the region which is the intersection of two boundary lines.
Hint:
Draw the lines
Given:
A corner point of a feasible region is a point in the region which is the _____ of two boundary lines.
Solution:
Let’s draw a line

We observe that we get the corner points after the intersection of the two boundary lines.
So, a corner point of a feasible region is a point in the region which is the intersection of two boundary line.

Linear Programming exercise Fill in the blanks question 8

Answer:

Maximum value=140
Hint:
Form the constraints coordinates (x,y)
Given:
The maximum value of $z=3x+4y$ subject to constraints $x+y\leq 40$,$x+2y\leq 60$,$x\leq 0$,$y\leq 0$ is _____
Solution:

From the constraints
$x+y\leq 40$
$x+y= 40$ … (i)

x	0	40
y	40	0

$x+2y\leq 60$
$x+2y= 60$ …..ii

x	0	60
y	30	0

Here,
$\begin{aligned} &x+y=40 \\ &x=40-y \end{aligned}$
Put $x=40-y$ in (ii)
$\begin{aligned} &40-y+2 y=60 \\ &40+y=60 \\ &y=20 \\ &\therefore x=20 \end{aligned}$
Now,
$\begin{aligned} &z=3 x+y \\ &A(20,20)=3(20)+4(20)=140 \\ &B(40,0)=3(40)+0=120 \\ &C(0,0)=0 \\ &D(0,30)=4(30)=120 \end{aligned}$
Therefore, maximum value =140 at (20,20)

Linear Programming exercise Fill in the blanks question 13

Answer:

In an LPP, the linear function which has to maximised or minimized is called a linear Objective function
Hint:
First know the LPP properties
Given:
In an LPP, the linear function which has to maximised or minimized is called a linear _____ function.
Solution:
In an LPP, the linear function which has to maximised or minimized is called a linear objective function.
Because, LPP is solved on the basis of objective and find its optimal solution. It cannot be constraints because it defined feasible region.
So, in an LPP, the linear function which has to minimised or maximized is called a linear objective function.

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