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APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 01 APSWRSCHOOL/JC, PVP
MONTH: NOVEMBER LINEAR PROGRAMMING
Date and Time: class: X Subject: Maths Medium: English
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
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Contentanalysis/concepts/sub
concepts
Activities indicating behavioral/learning out comesAids/experiments to bedone /demonstrations
etc.
method Evaluation
By teacher By Pupil
What do you call a first degree
equation in x and y?
What is the general form of
linear equation?Give an example for a linear
equation?
How many points do you need
to draw a line?
Can you say any two points on
the line 2x+3y=6?
How many parts do the line
divides a plane?
What are they?
If ax+by+c=0 is a line on the
plane what are the three parts?
What do you call ax+by+c>0
and ax+by+c0 and
ax+by+c++
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Recapitulation: 1) what is half plane divided by the line.2) What represents a linear in equation?
3) What is the convenient point to decide the half plane?
4) What is the solution set of system of linear in equations?
Behavioral changes: 1) pupil recognize the region form by the in equations.
2) Pupil finds the solution set of system of in equations.
Assignment: Exercise -1 problems 4 &5
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
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APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 02 APSWRSCHOOL/JC, PVP
MONTH: NOVEMBER LINEAR PROGRAMMING
Date and Time: class: X Subject: Maths Medium: English
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Contentanalysis/concepts/sub
concepts
Activities indicating behavioral/learning out comesAids/experiments to be
done /demonstrations etc.
method Evaluation
By teacher By Pupil
Convex set: X is a subset of
a plane. If XQP,
XPQ then X is calledConvex set.
A closed convex polygon in
the set of all points within
and on polygon with a finite
number of vertices.
1. What is a plane?
2. What are the closed figures in the
board?
3. We take a closed figure X in the
plane. How is the set of points of X
to the plane?
In the closed figure X, take any twopoints P, Q. Join the line segment
.PQ is it contains in X?
Is figure (2) convex set?
Why?
What is solution set of systemlinear equations?
What is the solution set of system
of linear in equations?
Draw the system of linear in
equations 5,0,0 + yxyx
What is the solution set?
Is it closed polygon?
Set of infinite points
X is subset of the plane
Yes. XPQ
No
XPQ/
points
OAB
yes
yes
(2)
Synthetic
Method.
What is LPP?
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Recapitulation: What is convex set?What is closed convex polygon?
What is open convex polygon?
What is objective function?
What is LPP?
What is the fundamental theorem on LPP?
Behavioral changes: pupil recognizes the convex set, closed convex set and open convex polygon?
Pupil recalls objective function and fundamental theorem.
Assignment: Find the maximum and minimum values f=4x+y at the vertices O(0,0),A(3,0),B(2,4),C(0,8).
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
7/21
APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 03 APSWRSCHOOL/JC, PVP
MONTH: NOVEMBER LINEAR PROGRAMMING
Date and Time: class: X Subject: Maths Medium: English
C l i / / b Aid / i
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Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
Maximize f=2x+3y subject to the
constraints0,0;93,5 ++ yxyxyx
What is a closed convex polygon?
What is an objective function?
What is the maximum value f=x+y
at the points
O(0,0),A(2,0),B(3,2),C(0,6)
What is linear programming
problem?
What is the fundamental theorem
on LPP?
Now we learn the graphical
method for solving LPP:
What is given?
What to do?
For maximize objective function
what to do first?
0,0 yx Which region we have
the sol tion?
The set of all points within and on
some polygon with a finite number
of vertices.
A function f=ax+by which is to beminimize or maximize is the
objective function.
6
A linear programming problem
consists of minimize or maximize a
function subject to certain linear in
equations.
The minimum or maximum of
f=ax+by occurs at least one of the
vertices of the polygon.
0,0;93,5 ++ yxyxyx
To maximize f = 2x +3y
We draw the graph of the given
system of in equations
1st quadrant
0,0 yx
So that system
has the solution
in 1st quadrant.
Points table for
x+y=5
5 0
Synthetic
method
What isgeneral form
of objective
function?
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Recapitulation: what are the steps to solve LPP by using graph?
Behavioral changes: pupil solves the linear programming problems
Pupil understands the graphical method to maximize the objective function.
Assignment: Exercise 2. Q.1, 2, 4, 5 and 10.
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
10/21
APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 04 APSWRSCHOOL/JC, PVP
MONTH: NOVEMBER LINEAR PROGRAMMING
Date and Time: class: X Subject: Maths Medium: English
C t t l i / t / b Aid / i t t b
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Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experiments to bedone /demonstrations etc.
method Evaluation
By teacher By Pupil
Maximize yxf 4+= subject to
the constraints
0,0
1234;4058
++
yx
yxyx
I thi LPP th l ti t i
What is LPP?
What are the steps to find tothe solution of LPP?
Now we learn the solution of
LPP using this graphical
method:
What we do first?
What is the region
represented by 0,0 yx ?
For Shading the half plane4058 + yx
What is the boundary line?
Tell me any two points on the
line?
Draw the line on the graph?
what is the solution set of?4058 + yx
Similarly what is the solutionset of 1234 + yx ?
What is the solution set of
given system?
Since solution set is closed
convex polygon, how do you
maximize?
Wh t th ti f
An LPP consists of
minimize or maximize a
function subject to the
constraints.
Draw the graph and find
vertices and maximize f
We draw the graph of in
equations
1st quadrant
4058 =+ yx
(5,0),(0,8)
Region which contains(0,0)
Region which does not
contains (0,0)
Closed convex polygon
ABCD
0,0 yx
Solution set in 1stquadrant.
Table for
8x+5y=40
x 5 0
y 0 8
?4058 + yx Represents half plane
which contains (0,0)
Boundary line of1234 +
?
Sysnthetic
method
What isobjective
function?
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Recapitulation: what are iso profit lines?What is the general form of iso profit line determined by objective function f=ax+by
What are the steps to solve LPP by general method?
Behavioral changes: Students understanding the difference of solving LPP methods.
Students draw the iso profit lines.
Students maximize or minimize LPP by general method if the solution set is not closed convex polygon.
Assignment: solve exercise 2 in the text book.
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
13/21
APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 05 APSWRSCHOOL/JC, PVP
MONTH: NOVEMBER LINEAR PROGRAMMING
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub Aids/experiments to be
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14/21
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experiments to bedone /demonstrations etc.
method Evaluation
By teacher By Pupil
Minimize f=4x+y subject to
the constraints
0,0
,82,6
++
yx
yxyx
What is the solution set of
system of linear in equations?
Are sure, it must be closed?
What is the feasible region?
What are iso profit lines?
If we draw iso profit lines
moving away from the origin
then how is value of f?
For finding minimum value of
f, how do you draw iso profit
lines?
What is the general method to
maximize f= ax+by subjet to
constraints.
Now we minimize f subject
to the constraints
What is the objective function?
What are the constraints?
What is the region denoted by0,0 yx ?
What are the boundary lines of
th h lf l
Convex set
No, either closed or open
The solution set of LPP is a
convex set called feasible
region.
Parallel lines determined by
objective function are callediso profit lines.
Value of f increases.
Moves closed to the origin
Graph the system and draw
iso profit line and move
towardsOrigin.
f=4x+y
0,0
,82,6
++
yx
yxyx
1st quadrant
82;6 =+=+ yxyx
0,0 yx Represents in
1st quadrant.
x+y=6
x 6 0
y 0 6
Synthetic
method
How iso profit
is lines eachother?
What is profit
line?
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Recapitulation: Describing the general graphical method to maximize f=ax+by?How do you draw iso profit lines?
Behavioral changes: Students understand the general method to minimize LPP.
Students find the method to various LPP problems.
Assignment: exercise 2 questions 6 ,7 &9.
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
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APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 06 APSWRSCHOOL/JC, PVP
MONTH: NOVEMBER LINEAR PROGRAMMING
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub Aids/experiments to
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
17/21
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experiments tobe done
/demonstrations etc.
method Evaluation
By teacher By Pupil
A manufacturer makes two
models A and B of a product.
Each model should be processedby two machines. To complete
one unit of model A, machines I,
II must work one hour and 2
hours respectively. To complete
1 unit of model B machines I, IImust work 4 hrs and 2 hrs
respectively. Machine I may not
operate more than 8 hours per
day. And machine II not more
than 10 hours per day. If the
profits on models A and B per
unit are Rs.200 and Rs.280respectively. How many units of
each model should be
manufacturer produce per day to
maximize his profit?
What is an objective function?
What is the LPP?
What are the steps to maximize f?
LPP problems arise in Business,
industry and transports. Now we
learn some application of LPP.
How many models are produced?
What are they?
To complete each model what
machines is used?
What is required in the problem?
Now we convert the given
conditions into in equations
Let the number of units A is x,
and units of B is y
Can number of models x and y be
negative?
H d d if
f=ax+by which to be
minimized or maximized.
Problem consists of
minimizing an objectivefunction f=ax+by subject to
constraints
Draw the graph. Find the
vertices of polygon; determine
the value of f of each vertex.
2
A & B
I & II
To maximize the profit of howmany units of each model
should be produced.
No
0,0 yx
Number of units of
A=x
No. units of B=y
X and y are nonnegative
0,0 yx
-------(1)
To make x , y units,
the machine I should
be work 1,4
hrs.respectively and
not more than 8 hours.
84
8)4()1(
+
+
yx
yx
--------(2)
A
N
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Recapitulation: What is given? What is required?What are the conditions to maximize the profit?
Maximize P=200x+280y subject to above constraints?
Behavioral changes: Students understand that LPP problems are used in industry.
Students apply their knowledge into realistic problems.
Assignment: exercise 3. Q1
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APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 07 APSWRSCHOOL/JC, PVP
MONTH: NOVEMBER LINEAR PROGRAMMING
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub Aids/experiments to be
7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (2)
20/21
y pconcepts Activities indicating behavioral/learning out comes
pdone /demonstrations
etc.
method Evaluation
By teacher By Pupil
A shop keeper sells not morethan 30 shirts o each colour. At
least twice as many white ones
are sold as green ones. If the
profit on each of the white be
Rs.20, and that of green beRs.25, how many of each kind
be sold to give him a
maximum profit?
What is the LPP?
What we do in LPP?
Where do LPP problems arise?
Now we learn an LPP
What are given conditions in
this LPP?
What is required?
What kind shirts are sold?
Let No. white shirts are x No.
green shirts are y
Can x, y be negative?
Represent symbolically?
What are the conditions be
given?
He sells x, y and not more than
thirty. Can you express this in
in equation?
What is next condition?
Problem consists of
minimizing an objective
function f=ax+by subject to
constraints
Maximize are minimize an
objective function
In business, industry
How many kind of eachcolored shirts be sold to give
maximum profit
White and green
No
0,0 yx
He sells not more than 30
totally.
30+ yx
At least twice as many white
ones are sold as green.
Let No. white shirts arex No. green shirts are y
x, y are non negative0,0 yx
---------(1)
Sum of x an y not
more than 30
therefore
30+ yx
--------(2)At least twice as many
synthetic
method
A
N
If x is non
negativerepresent
symbolically?
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Recapitulation: What is the maximizing function in this problem?What are the conditions to maximize the profit?
What are the exact linear in equation for given data?
Behavioral changes: Students apply the concept of LPP into the real life.
Assignment: exercise 3 question NO.3
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