1. The document discusses canonical form and standard form of linear programming problems (LPP). Canonical form requires the objective function to be of maximization form, all constraints to be less than or equal to type, and all variables to be non-negative. Standard form additionally requires right sides of constraints to be non-negative and constraints to be expressed as equations using slack or surplus variables. 2. The key difference between canonical and standard form is that standard form represents constraints as equations using slack/surplus variables while canonical form uses inequalities. Standard form simplifies the canonical form for applying the simplex method of solution. 3. Linear programming techniques allow managers to optimize objectives like profit maximization and cost minim

1. S
Subject:-
Topic::- Canonical form and Standard
form of LPP
Under the guidance of
Sundar B. N.
Asst. Prof. & Course Co-ordinator
GFGCW, PG Studies in Commerce
Holenarasipura

2. GGa
Presented By,
UNIVERSITY OF MYSORE
G.F.G.C for
WOMEN,
PG
STUDIES
IN
COMMERC
E

4. Introduction of LPP
Canonical form of LPP
Standard form of LPP
Difference Between Canonical form and
Standard form of LPP
Conclusion
Reference
Content:

5. Introduction:
The hand account is an
indispensable necessities of life.
It is used to record what is
happening in your daily life.
The hand account is an
indispensable necessities of life.
It is used to record what is
happening in your daily life.
LPP:
Linear programming is a method to
achieve the best outcome in a mathematical
model whose requirements are represented by
linear relationships. Linear programming is a
special Case of mathematical programming.
The hand account is an
indispensable necessities of life.
It is used to record what is
happening in your daily life.
.
LPP

6. LPP
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7. Canonical Form:-
LPP

8. Characteristics of canonical form:
Characte
ristics of
canonica
l form
1.Objective function should be of maximisation from. If it is given in
minimisation from, it should be converted into maximisation form.
2 .All the constraints should be of " ≤type, except for non-negative
restrictions. Inequality of "≥ type if any , should be changed to on
inequality of the "≤type (by multiplying both the side of - 1)
3. All variables should be non - negative - difference of tow non-
negative variables
4. Canonical form of a set of linear equation will be discussed next.
5. Canonical from of LPP is essential for simplex method.
6. This is know as canonical form of LPP.
LPP

9. Example (problem):
Minimize the Z = 2x + y + 6z
Subject to constraints :
4x + 3y + z ≤5
2x - y + 3z≤7
x +5y≤3
X, Y. ≥ 0 and z is unrestricted in sign
LPP

10. ≤
Solution:
Step1: Objective function (of)
Minimize z =2x + y +6z
Now we have to minimize
- z = -2x - y - 6z
Maximize the z'= -2x - y - 6z
Where z'= -z
Step2: consider > constraints
So now consider 1st constraint
(Multiplied by - 1)
4x + 3y + z > 5 (x-1)
=-4x - 3y - z < -5
Minimize the Z = 2x + y + 6z
Subject to constraints :
4x + 3y + z ≤ 5
2x - y + 3z ≤7
x +5y≤3
X, Y > 0 and z is unrestricted in
sign
Note:
In this presentation we consider,
< is . ≤
> is. ≥

11. Minimize the Z = 2x + y + 6z
Subject to constraints :
4x + 3y + z < 5
2x - y + 3z <7
x +5y < 3
X, Y > 0 and z is
unrestricted in sign
Step3: Final mathematical
formulation
Maximize the z'= -2x - y - 6z
Subject too Constraint
-4x - 3y - (z-z) I < -5
2x-y +3(z-z) < 7
x + 5y < 3
Non-negative restriction
x > 0, y > 0, z > 0, z > 0
LPP

13. • It is developing general procedure problem.
• It is standard procedure.
• It is simplexed procedure of canonical form
• It is a simplified version of canonical form
Picture
LPP

14. The hand account is an
indispensable necessities
of life. It is used to record
what is happening in your
daily life.
nsable necessities of life.
It is used to record what
is happening in your daily
life.
The hand account is an
indispensable necessities
of life. It is used to record
what is happening in your
daily life.
Characteristics of Standard Form:-
1 - The objective function should be of maximisation form.
2 - The right side element of each constraint should be
non-negative (if not X-1)
3 - All constrains should be expressed in the form of
equations (equalities), I expect for the non-negative
restrictions by augmenting slack or surplus variables
!).For inequalities of the of the "<" I type, we add the slack
variables
||)If the inequalities are of the ">" type, we subtract
surplus variables
LPP

17. Step 3: Inequalities are to be converted
To equations
-2x + y + s1 =4
X + 2y + z - s2 =5
2x + 2z + s3 =2
Step 4 : Standard form of LPP
maximize Z'= -2x - y - 4z + s1 - s2 +s3
Subject to the constraints
- 2x + 4y + s1 =4
X +2y + z - s2 =5
2x + 3z + s3 = 2
Non - negatives
X > 0, Y > 0, Z > 0, S1> 0, S2 >0, S3 > 0
LPP

18. Standard form:
1. Sandard form is a
simplified version of
canonical form that
represents boolean outputs
of digital circuit's using
boolean Algebra.
2 . Simple
Canonical form:
1.canonical from is a way of
representing boolean outputs
of digital circuits using Boolean
algebra
2.More complex
Difference
between
canonical
form and
standard
form :•

19. Standard form and canonical form of
LPP:
* A given linear program can be put in different equivalent
form by suitable Manipulation. Two forms in particular will be usefu
These are the standard and canonical form, A linear program is
said to be in standard format is all restrictions are e qualities and al
variables are non negative. The simplex Method is designed to be
applied only after the problem is putting in standard form

20. * A minimisation problem is in canonical form
is all variables are non negative and all constraints are
of the type. A maximisation problem is in canonical
form is all variables are non negative and all
constraints are of the type. A maximisation problem is
IN canonical form is all variables are none negative And
all constraints ate of the type.

21. Conclusion:
Linear programming is very important
Mathematical technique which enables Manager to
arrive at proper decisions regarding his area of work.
Thus it is very important part of operation research .
The main objective is to maximisation of
profit and minimisation of cost. It is very useful for
optimization solution.
LPP

23. Reference:-
 https://www.matem.unam.mx/~omar/math340/s
td-form.html
 https://youtu.be/PJG8zj5YkpI
 https://youtu.be/fvTHjfxKgz0
 https://www.slideshare.net/shamjithkeyem/num
erical-analysis-canonical
 https://pediaa.com/what-is-the-difference-
between-canonical-and-standard-form/