Theortical or probability distribution
Advantages of theortical or probability distribution
Binomial distribution and its main features
Poisson distribution and its main features
Explaination of normal distribution in deep and scholarly study base
Importance of Normal Distribution
Thursday, December 11, 2008
Lesson 1 - Linear programming
Linear programming
Limitation of linear programming
Importance of linear programming
Q: - What is non negative restrictions in LPP
Graphic method of solving linear programming problem
Simplex table method of linear programming
Q: - What is linear programming problem. ? How can create the structure of linear programming?
Limitation of linear programming
Importance of linear programming
Q: - What is non negative restrictions in LPP
Graphic method of solving linear programming problem
Simplex table method of linear programming
Q: - What is linear programming problem. ? How can create the structure of linear programming?
Sunday, December 7, 2008
Correlation
While studying the characteristics of a series involving only a single variable , which we generally call as univariate distribution , we have to restrict ourselves to find the measure of central tendency , its variation and skewness etc. Whenever the idea of bivariate distribution or a multivatiate distribution comes into our mind the very first desire which arises is to know as to how they are related to each other . If some how or desire which arises is to know as to how they are relate to reach other our next issue will be to know the extent of their relationship . The relationship between two series which are quantitatively measured is know as correlation . Here we must distinguish between the two words correlation and association . Correlation is the relationship between two or more series which are quantitatively measured where as association refers to the relationship between the series which are qualitatively measured .
Although we have to use some mathematical formulae to know and confirm extent of correlation between two or more variables but the issue is so common and popular that we do not have to stain ourselves to judge the behavior of the series with regards to their relation with each other .
Sir francis galton was one of the first of few statisticians who developed the technique of establishing the concept of correlation graphically in 1896 . Karl pearson was the one who introduced the formula based on mathematical treatment and established the extent of correlation . It was logically as well as other wise proved that if two or more quantities vary in sympathy so that movement in the one tend to be accompanied by corresponding movement in the other then they are said to be correlated
Although we have to use some mathematical formulae to know and confirm extent of correlation between two or more variables but the issue is so common and popular that we do not have to stain ourselves to judge the behavior of the series with regards to their relation with each other .
Sir francis galton was one of the first of few statisticians who developed the technique of establishing the concept of correlation graphically in 1896 . Karl pearson was the one who introduced the formula based on mathematical treatment and established the extent of correlation . It was logically as well as other wise proved that if two or more quantities vary in sympathy so that movement in the one tend to be accompanied by corresponding movement in the other then they are said to be correlated
Tuesday, December 2, 2008
Importance of Normal Distribution
1. Helpful in statistical quality control
normal distribution is very useful for controlling the quality in business. With this we can fix the limit of quality . that will helpful for controlling the quality .
2. Helpful in forecasting
It is very helpful we can calculate the estimated length of the bones of animals and woods and leaves . because if animals are one type their numbering is normally distributed .
3. Helpful making mean as normal distribution :-
if we take one sample out of the universe and calculate the mean size of growing then it will normal distribution
normal distribution is very useful for controlling the quality in business. With this we can fix the limit of quality . that will helpful for controlling the quality .
2. Helpful in forecasting
It is very helpful we can calculate the estimated length of the bones of animals and woods and leaves . because if animals are one type their numbering is normally distributed .
3. Helpful making mean as normal distribution :-
if we take one sample out of the universe and calculate the mean size of growing then it will normal distribution
Explaination of normal distribution in deep and scholarly study base
I am explaining all of the normal distribution in deep and scholarly study base . Actually this concept is some difficult for commerce students or non math group but learning can learn every thing .
In binomial and possion distribution we can calculate theoritical distribution in discreate series form . But continueous series is also so important . Normal distribution is utilized in calculation of distribution in contineous series .
" Normal distribution is useful to study and analysis of continous series."
This concept is discovered first by An English mathematician De - Moivre in 1754 . From 1777 to 1855 , german mathematician used it in physics . Now currently it in solving business problems.
Freatures or characterstics of Normal distribution
In binomial and possion distribution we can calculate theoritical distribution in discreate series form . But continueous series is also so important . Normal distribution is utilized in calculation of distribution in contineous series .
" Normal distribution is useful to study and analysis of continous series."
This concept is discovered first by An English mathematician De - Moivre in 1754 . From 1777 to 1855 , german mathematician used it in physics . Now currently it in solving business problems.
Freatures or characterstics of Normal distribution
- Value of n is very large.
- p and q are very small.
- If m is very large . It is the limiting case of poisson distribution
- Graphical presentation
5 .Normal curve is always bell shaped
6. Normal Curve has only one mode
7. Q3 - m = m - Q1
8. mean = median = mode
9. rang = +/- .6745 = 6 X S.D.
10. Quartile deviation = probable erro
11. Curve always on x-axis
12. Probable error = .845 of s.d.
13. Normal curve 's arear actually is the area of total probability area . That is always one and one side of curve is 0.5 and other side of mean is 0.5
14. The area corressponding to z >0 or z <>
15. z = x-m/ standard deviation
Tuesday, November 25, 2008
Poisson distribution and its main features
Poisson distribution is main concept of theoretical distribution which is invented by Simeon Denis Poisson . In this distribution some of the good points which we can not get in binomial distribution . In other worlds it birth due to some of weak points of binomial distribution . The main limitation of binomial distribution is that we can not calculate distribution if n is infinite and probability of success is very low . At these situation we can calculate Poisson distribution .
Formula of calculating Poisson distribution
p(r) = e's power -m multiply with m's power r and both divided by r!
m = mean or average of distribution
mean can be calculated = total of fx divided by total of f
r = respective no. of trial
e = is the base of natural logarithm = 2.7183
for more detail of probability distribution
Formula of calculating Poisson distribution
p(r) = e's power -m multiply with m's power r and both divided by r!
m = mean or average of distribution
mean can be calculated = total of fx divided by total of f
r = respective no. of trial
e = is the base of natural logarithm = 2.7183
for more detail of probability distribution
I am also giving poisson distribution tutorial in video of bionicturtledotcom
you can see and understand the concept of poisson distribution
Binomial distribution and its main features
Q:- What is binomial or Bernoulli distribution ? Explain its with example and explain its main features ?
Ans. Binomial distribution is a theoretical distribution . It is invented by James Bernoulli . So its other name is Bernoulli distribution .
Binomial means two names . Every probability distribution has two things , one is success and other is failure . This distribution can be calculated with formula given in picture .
get more information of probability distribution Sunday, November 23, 2008
Advantages of theortical or probability distribution
There are following benefits of theoretical or probability distribution
1. Where the calculation of observed distribution is not possible :-
Sometime observed base distribution's calculation is not possible due to impossibility at that place we can calculate probability distribution.
2. Helpful in forecasting :-
This probability distribution is very helpful for forecasting and on this basis we can estimate our future and make good plans for our business.
3. Helpful in Comparison :-
We can compare it with observed or real distribution and evaluate our efficiency of work.
1. Where the calculation of observed distribution is not possible :-
Sometime observed base distribution's calculation is not possible due to impossibility at that place we can calculate probability distribution.
2. Helpful in forecasting :-
This probability distribution is very helpful for forecasting and on this basis we can estimate our future and make good plans for our business.
3. Helpful in Comparison :-
We can compare it with observed or real distribution and evaluate our efficiency of work.
Theortical or probability distribution
Q: - Define theortical or probability distribution ? Give its advantages?
Ans. Theortical distribution is that distribution which calculated by some formula. Because these distribution is probability base so this is also know as probability distribution.
there are three methods of calculating theortical distribution :-
☺ Binomial Distribution
☼ Poisson Distribution
☺ Normal Distribution
Ans. Theortical distribution is that distribution which calculated by some formula. Because these distribution is probability base so this is also know as probability distribution.
there are three methods of calculating theortical distribution :-
☺ Binomial Distribution
☼ Poisson Distribution
☺ Normal Distribution
Monday, October 20, 2008
Why Fisher Index number is So Ideal Index Number
Fisher has discovered weighted index number in which he try to calculate best index number because he has taken both current and past years quantity as the base of price index number.
The main quality of fisher index number is that it qualify both time reversal test and factor reversal test.
- Time reversal test means
P01 X P10 = 1 , It means if we changes time of fisher formula current period into base year and base year in to current year and when we multiply both index number it must equal to 1.
- Factor reversal test
If we changes price into quantity and quantity into price.Then we calculate index and then we multiply , it must equal to value Index. Fisher pass this test
So above reason fisher index is best.
Learn this Concept with More Detail at here.
Monday, October 13, 2008
What do you know about Index number
Definition of Index Number :Index numbers are special type average which shows the changes in price and quantity due to changes in time and place . Without calculating index number , we can not make our national plannings . So index number is very important for us. Because index number can gives us clear picture of increasing the prices of any country or decreasing . If index numbers shows that prices are increased from base years more than 20% , then we can start different progressive plannings for safeguarding poor families by giving free food facilities. In calculating index number fisher index number is better than other weighted aggregated indices.
In last we can define that if current year prices divided by previous years prices and multiply with 100 . What will come , we generally called index number . Then we compare this index number with 100 and calculate what is percentage of increasing or decreasing the price.
Semi Average method
2nd method of measuring Trend – Semi Average method
Under this method, we can calculate trend. For this, you have to show your time series on graph paper. For this time is on x’ax and data like sale , production is on y’ax now make original graph by plotting point on graph paper by seeing time and value of data. After plotting original data , now you can calculate trend line . For calculating trend line , you have to calculate semi average . Semi average means average between two time period .
Here are two method of calculating semi average of data which are given below:-
1st method is use when data is even
In this case all time series divides in to two parts and then we calculate average of each part suppose if you have 10 years data then you divide into 5 -5 years half and then you will calculate first five year average and then next five year average after this you have to plot this on the graph paper . This will show the trend line .See picture and understand
2nd method is used when data is odd -
→ in this method you just live middle data and the follow above procedure
Under this method, we can calculate trend. For this, you have to show your time series on graph paper. For this time is on x’ax and data like sale , production is on y’ax now make original graph by plotting point on graph paper by seeing time and value of data. After plotting original data , now you can calculate trend line . For calculating trend line , you have to calculate semi average . Semi average means average between two time period .
Here are two method of calculating semi average of data which are given below:-
1st method is use when data is even
In this case all time series divides in to two parts and then we calculate average of each part suppose if you have 10 years data then you divide into 5 -5 years half and then you will calculate first five year average and then next five year average after this you have to plot this on the graph paper . This will show the trend line .See picture and understand
2nd method is used when data is odd -
→ in this method you just live middle data and the follow above procedure
Friday, October 10, 2008
Main Components of Time Series
What are the main components or methods of time Series
- Secular trend or Trend method :-
Secular trend is basic tendency to grow or decline over a period of time. Its other name is trend or long term trend .In this trend we ignore short term fluctuations but we see the tendency of data in long period
◘ Trend may be up-word or down word
◘ If we show the trend series on the graph paper , we will take time on x’ax and data on y’ax and make the trend live .This trend line is called linear line .
◘ In maths language linear line = y = a+bx if b is positive the trend will positive .If b is negative trend will be negative.
Measurement /Method of trend :-
i) Free hand graphic method:-
In this method we can get trend by making graph on x’ax , we take time and on y’ax we take the data after this we plotted original points . After this a smooth straight line is drawn passing between the original graph . This line is called trend line .
Time Series and its importance for business
Q: - What is the time series? What is the main importance of time series? What are its essential elements?
Ans: - Definition of time series:-
The set of data depend on time is called time series. If any data is collected on base of time and make a series that series is called time series .
Importance of Time series:-
There are many benefits of time series which can be written by us for business purposes
♠ Helpful for study of past behaviour
Time series are very helpful in study of past behaviour of business .On this basis , we can invest our money in that type of business. It is duty of businessman to make time series of past sale or profit and see what is the trend of sale or profit in that type of business.
♠ Helpful in forecasting
Forecasting is science of estimation. Today is the day of competition so if you have to win from competition then you must learn this science , this science can be utilized if we make time series and on the basis we can read the history and then we can decide what happen in future . Suppose if we can make the time series of past strategy of our competitor then on this basis we can estimate future strategy of our competitor and on this base we can change our strategy for defeating our competitor.
♠ Helpful in evaluating the achievements:-
Time series is an equipment in your hand on this basis you can evaluate your business achievements if you did good , your performance shows your good face in the time series by up-word trend of your performance. If your business performance is very bad then you can make new policies to stable your business.
♠ Helpful in comparison:-
If we can calculate our two or more branches time series then we can compare the performance of our branches. On their performance we can give them rewards.
♠ Essential of Good time series:-
1. Data must be for a sufficient period
2. Equal time gap
3. constant or normal period.
Ans: - Definition of time series:-
The set of data depend on time is called time series. If any data is collected on base of time and make a series that series is called time series .
Importance of Time series:-
There are many benefits of time series which can be written by us for business purposes
♠ Helpful for study of past behaviour
Time series are very helpful in study of past behaviour of business .On this basis , we can invest our money in that type of business. It is duty of businessman to make time series of past sale or profit and see what is the trend of sale or profit in that type of business.
♠ Helpful in forecasting
Forecasting is science of estimation. Today is the day of competition so if you have to win from competition then you must learn this science , this science can be utilized if we make time series and on the basis we can read the history and then we can decide what happen in future . Suppose if we can make the time series of past strategy of our competitor then on this basis we can estimate future strategy of our competitor and on this base we can change our strategy for defeating our competitor.
♠ Helpful in evaluating the achievements:-
Time series is an equipment in your hand on this basis you can evaluate your business achievements if you did good , your performance shows your good face in the time series by up-word trend of your performance. If your business performance is very bad then you can make new policies to stable your business.
♠ Helpful in comparison:-
If we can calculate our two or more branches time series then we can compare the performance of our branches. On their performance we can give them rewards.
♠ Essential of Good time series:-
1. Data must be for a sufficient period
2. Equal time gap
3. constant or normal period.
Wednesday, October 8, 2008
Definition of Annuities
Annuities are the installments when any asset or loan is taken. Then this duty of buyer or loan taker to give repayment in installments. Those installments are called annuity.
Formula of Annuity
Annuity = Principal amount / {(1+r / 100)t -1 / /100)
Our Mission
Our mission is give free education not only in business mathematics but in every field. This website and my other website is just little try to fulfillment of our mission.
- Mission for students
Why are the teachers charging high fees from students and their parents by blackmailing them that they are teaching them .Even then they take double money from them on the name of tuition? This is real injustice with dear students. I am against with this trend. I am trying to abolish this trend by using online as one of my tool. - Mission for businessmen
Businessmen are the men who take all the risk of business. Then why do they suffer losses. This is not good. The main reason behind this they do not know business mathematics. If they will know the complete fundamentals of business mathematics, they will surely gain profit from their business. Because in mathematics, there are lot of worthless bundle of knowledge which can give wonderful techniques to businessmen that how to they produce in what quantity. At what price they want to sell their products so that the cut off the competition. Different assignment techniques, transport solution, linear programming simplex and graphic method, interest rates formulae, depreciation calculation and so many formulae in the math which they gives us direction to develop our business and production . By operating this website, I am trying to help to my dear businessmen, entrepreneurs, companies, manufacturers, agriculturers, small traders, firms and shopkeepers in growing their business.
If I am taking this holy mission then your duty is also to take part in this mission, just write your mathematical problems to me at my email id vinod_13242002@yahoo.com , I and my team try to best for solution of your maths problem. Or you can give your view and opinions by giving your comments on the given articles .This comments, view and your opinions are also the part of our mission.
About Me
I am the lover of maths subject. My name is Vinod Kumar. From beginning of my life, I have liked mathematics. But because of my career became in the business study. So I learnt business mathematics. In my study time, I faced so many difficulties in business mathematics which I solved in my teaching time. But today when I have started this website, I am enjoying solving the maths and writing this solution in my free business mathematics website. I am writing article just telling you how to solve difficult business problems with easy maths calculations. I do not declare fully correctness in my solution because man is name of mistakes but, believe me that I am doing hard work day and night for giving you the best solution of your all business problems with the help of mathematics .I am trying to give best definitions of all mathematical terms so that you can get confidence in maths. I am not PhD. Holder in mathematics but because of I am lover of maths and due to I think every scholar has right to get free basic knowledge in the field of mathematics , So that when he will do his work in any field for any purpose , he will gives his correct maths calculations . That correctness, I want from my society, from my country people, from this world. Honesty, duty, brotherhood, helpfulness, good feelings, love, devotion, correctness, learning from mistakes, development, growth, profit, benefits, advantages, in end all good and moral things in whole world is inter-connect with maths . I am just trying to make relationship these moral values with my selflessness, free and voluntary for the benefit of middle and weak and learner in this world. I hope you will like my own introduction with you. Please give me your reaction with about me and my website in my email id vinod_13242002@yahoo.com
Tuesday, October 7, 2008
Calculation of Difficult sum with the use of logarithm
Dear friends
Logarithm is mathematical series with this we can calculate difficult sums. With calculator, we can not solve this sum so we need logarithm to solve these problems. Here I am giving you how to solve difficult problems with the help of log .
1st step
Suppose x = (32.38)1/7
2nd step
Take the log both sides
Log x = log (32.38)1/7
Log x = 1/7 log (32.38)
Now we see that 32.38 has 2 digit before point so we calculate the number before point
That is 2-1 =1
1 is written before point
As
And then we calculate value of log of 32 in 3 in logarithm see it and then see in 8 in last columns
You will find 5092 and 9
Add it = 5101
Now we write in
Log x = 1/7 (1.5101)
Or log x = 1.5101/7 =0.22
Now both side put antilog
In left side log cancel with antilog
X= antilog 0.22
Now because o is before point so we add one in it and then we find 0+1=1 , it means after calculating antilog we will put point after one digit from left side.
See the antilog of 0.22 in antilog table
That is 1660
Now put point after one digit that is 1.660
Your answer is x =1.660
Logarithm is mathematical series with this we can calculate difficult sums. With calculator, we can not solve this sum so we need logarithm to solve these problems. Here I am giving you how to solve difficult problems with the help of log .
1st step
Suppose x = (32.38)1/7
2nd step
Take the log both sides
Log x = log (32.38)1/7
Log x = 1/7 log (32.38)
Now we see that 32.38 has 2 digit before point so we calculate the number before point
That is 2-1 =1
1 is written before point
As
And then we calculate value of log of 32 in 3 in logarithm see it and then see in 8 in last columns
You will find 5092 and 9
Add it = 5101
Now we write in
Log x = 1/7 (1.5101)
Or log x = 1.5101/7 =0.22
Now both side put antilog
In left side log cancel with antilog
X= antilog 0.22
Now because o is before point so we add one in it and then we find 0+1=1 , it means after calculating antilog we will put point after one digit from left side.
See the antilog of 0.22 in antilog table
That is 1660
Now put point after one digit that is 1.660
Your answer is x =1.660
Tuesday, September 30, 2008
Define Compound Interest
Compound Interest is differ from simple interest .If we calculate interest on principal with previous year interest , then calculated interest is called compound Interest.
Formula of Compound Interest =P[( 1+R/100) and its power t - 1 ]
suppose Principal =Rs.8000
rate of compound Interest =5%
Time = 2 year
Compound Interest = P[( 1+R/100) and its power t - 1 ]
C.I.= 8000[(1+5/100) and its power 2 -1]
C.I.=Rs. 820 /-
Formula of Compound Interest =P[( 1+R/100) and its power t - 1 ]
suppose Principal =Rs.8000
rate of compound Interest =5%
Time = 2 year
Compound Interest = P[( 1+R/100) and its power t - 1 ]
C.I.= 8000[(1+5/100) and its power 2 -1]
C.I.=Rs. 820 /-
Definition of Simple Interest and its formula
Simple Interest is the interest on principal when we do not see the next year interest or include for calculation of such interest.
Calculation of Simple interest is very easy:-
Formula of Simple Interest =Principal Amount X Rate/100 X time
Or
S.I.= P x R/100 x t
For example :-
Ram gives the loan to sham Rs. 10000 for 5 years @ 10 % simple interest
Calculate simple interest .
Solution:
Simple Interest = P x R/100 x t =10000 x 10/100 x 5 = RS .5000 /-
Calculation of Simple interest is very easy:-
Formula of Simple Interest =Principal Amount X Rate/100 X time
Or
S.I.= P x R/100 x t
For example :-
Ram gives the loan to sham Rs. 10000 for 5 years @ 10 % simple interest
Calculate simple interest .
Solution:
Simple Interest = P x R/100 x t =10000 x 10/100 x 5 = RS .5000 /-
Tuesday, September 23, 2008
Linear programming
Decision making has always been very important in the business and industry world . A production manager is always thinking about the commodities to be produced and the quantities of each commodity to be produced . He is also very particular on the processes to be applied . Alfred marshall feels that the businessman by his trained instinct rather that with formal calculations tries to minimize the cost function . But now there does exist a method of formal calculations often termed as linear programming . Russin mathematician Mr. L.V. Kantorovich was the first to formulate this method . But in 1947 George B. Dantzig developed it for the purpose of scheduling the complicated procurement activities of the united states air force.
Today this method is being used in solving most of business problems . Electronic computers have increased its applications to solve many other problems in industry.
Meaning of linear programming
The word linear means that the relationship handled are those represented by straight lines , the relationships are of the form y = mx +c and the word programming means taking decisions systematically .Thus linear programming is decision making technique under given constraints on the assumption that the relationships amongst the variables representing different phenomena happen to be linear . In other words,” linear programming is the maximization or minimization of a linear function of variables subject to a constraint of linear inequalities .”
In simple words , linear programming is a mathematical technique for finding the optimum solution to a linear function of two or more decision variables subject to a set of linear constraints .The linear function to be optimized is called the objective function .
Today this method is being used in solving most of business problems . Electronic computers have increased its applications to solve many other problems in industry.
Meaning of linear programming
The word linear means that the relationship handled are those represented by straight lines , the relationships are of the form y = mx +c and the word programming means taking decisions systematically .Thus linear programming is decision making technique under given constraints on the assumption that the relationships amongst the variables representing different phenomena happen to be linear . In other words,” linear programming is the maximization or minimization of a linear function of variables subject to a constraint of linear inequalities .”
In simple words , linear programming is a mathematical technique for finding the optimum solution to a linear function of two or more decision variables subject to a set of linear constraints .The linear function to be optimized is called the objective function .
Limitation of linear programming
No doubt with linear programming , we can calculate optimum solution of our business problems , but there are several problems or limitations in this techniques :-
- For calculation solution it is necessary that variables must be related with each other but when we see in real world , then we get no such relations .
- Uncertainty is forgotten in this techniques but in real world we see uncertainty in every work
- This is the day of fluctuations , so there is not constant rate of cost or rate of profit or rate of sale in business . So calculating of solution with this technique is very difficult .
- Every business has own problem which is different from other business so solution of one business problem can not same apply on other business . So solution of problem is time consuming .
Importance of linear programming
Dear friends
There are many benefits of linear programming for business
1. Solve the business problems
With linear programming we can easily solve business problem. It is very benefited for increase the profit or decrease the cost of business.
2. Easy work of manager under limitations and condition :-
Linear programming solve problem under different limitions and conditions , so It is easy for manager to work under limitations and conditions . It helps manager to decide in different limitations.
3. Use in solving staffing problems:-
With linear programming , we can calculate the number of staff needed in hospitals ,mines , hotels and other type of business.
4. Helpful in profit planning :-
Today linear programming is using for good profit planning.
5. Select best advertising media
With linear programming we can select best advertising media among a numbers of media.
6. solve the diet problems :-
With linear programming you can solve the diet problems with minimum cost. It is very useful for hospitals .There are different elements like vitamins, proteins, carbohydrates etc. You can select best quantity of them with minimum cost.
There are many benefits of linear programming for business
1. Solve the business problems
With linear programming we can easily solve business problem. It is very benefited for increase the profit or decrease the cost of business.
2. Easy work of manager under limitations and condition :-
Linear programming solve problem under different limitions and conditions , so It is easy for manager to work under limitations and conditions . It helps manager to decide in different limitations.
3. Use in solving staffing problems:-
With linear programming , we can calculate the number of staff needed in hospitals ,mines , hotels and other type of business.
4. Helpful in profit planning :-
Today linear programming is using for good profit planning.
5. Select best advertising media
With linear programming we can select best advertising media among a numbers of media.
6. solve the diet problems :-
With linear programming you can solve the diet problems with minimum cost. It is very useful for hospitals .There are different elements like vitamins, proteins, carbohydrates etc. You can select best quantity of them with minimum cost.
Monday, September 22, 2008
Q: - What is non negative restrictions in LPP
Ans.
Non negative restrictions mean that both the value of x and y must be zero or more than zero. Suppose businessman wants to know what unit of ice cream and chocolate. But its value must be zero or more than. This is basic condition of linear programming.
In math we can write it as x, y >- 0
Non negative restrictions mean that both the value of x and y must be zero or more than zero. Suppose businessman wants to know what unit of ice cream and chocolate. But its value must be zero or more than. This is basic condition of linear programming.
In math we can write it as x, y >- 0
Thursday, September 18, 2008
Graphic method of solving linear programming problem
Graphic method is very scientific method of solving linear programming problem. A producer wants to produce two goods but he is in confusion about the quantity of the product . In graphic method we make the graph of all condition for achieving our objective . For making graph we deem first x as zero and then we can calculate the value of y .Then we calculate y as zero and we calculate x's value on this base we make graph on the graph paper . When we see the condition and on this base we calculate our feasible area .
Dear , feasible area is area which satisfy all the conditions. We calculate its all point .Then these value of x and y put in our objective function . Which x and y 's value satisfied our objective . That will be our solution . Maximizing of our profit or minimizing our loss is our main objective.
Wednesday, September 17, 2008
Simplex table method of linear programming
Dear friends ,
Simplex or simplex table method of linear programming is very scientific method of solving business problem . It is very complex but its name is simplex . Because after using this we can solve all difficult business problems. In this method we make simplex table . It may make 1,2,3or more simplex table until value of zj – f 1 is not equal to zero or positive . If simplex table give zero or positive value of zj – f 1 then we can easilty calculate the quantity of our two products . Other steps see in picture .
Q: - What is linear programming problem. ? How can create the structure of linear programming?
Dear friends ,Linear programming problem is structure in which we solve our business problem. It is benefited to us to make the structure of linear programming for best utilization of our skills in business.
Step 1
Determination of our objective
Either we want to maximize our profit or minimize our cost .
This is called z in the math language . Fix the profit or cost rate for your two product . This is called c1 and c2 and and multiply with x1 and x2 the quantity of our two product
Here is
Our objective function
Z= c1 x1 + c2 x2
Step 2
Determination of our condition in achieving our objective
Condition means we can achieve our objective with in our limit , suppose we have limited money , our labourer limits , our machinery capacity have some limit , or we have limited time . So identity this and write below.
a11 x1 + a12 x2 <> 0
After formulation of linear programming problem . We can calculate both product quantity either with using graphic method or simplex table method .
linear programming
Dear friends ,
Linear programming is mathematical technique, with this we can solve mathematical problems. In other words, it is the mathematical method which is used for maximum utilization of limited source of business. It is very scientific way in which we get our objective with given conditions and constraints .
There are lot of business problem in which math is used . Suppose if you want to produced two product, A and B . Now, you want to know , what quantity of A and B , you will produced so that you can either maximum profit or minimum cost . Solving of this problem is only with the help of linear programming. So , it is very necessary to manager or businessman to get the education of linear programming .
Friday, September 12, 2008
Properties of Determinants
Here , I am giving you the full detail of properties of determinant for your education purpose . The following properties are very helpful for commerce student to calculate value of determinant without using of expending procedure .
Just remember and use following properties of determinants :-
Just remember and use following properties of determinants :-
- If we transpose of any matrix and then calculate the value of determinants, there is no difference between original value and transposed matrix’s determinant.
- If all the elements of any one column or row of any matrix are zero, then the value of determinant must be zero.
- If any two rows or column’s all value are same then the value of determinant must be zero.
- If any two rows or column of any matrix are proportionate, then the value of determinant must be zero.
- If we multiply any row or column with any scalar, its value of determinant will also multiply with same scalar.
- If take any common factor from any column and write outside the matrix then the values of determinant never change.
- If we calculate the value of any diagonal matrix then it always equal to the multiplication of its all main diagonals.
Wednesday, September 3, 2008
What is determinant
Determinant is square matrix .But it is bounded by two bar lines not two brackets .We can easily calculate the value of determinant .It is called expand of determinant .Here I am showing you the picture of formula of determinant .Determinant is very useful for calculating inverse of matrix and adjoint of matrix . Because co-factor for adj. only calculate in determinant not in matrix .
Tuesday, September 2, 2008
Addition and substraction of two matrix
Dear friends ,
Addition and substraction of two or more matrix is very easy . If You have two or more matrix or same order , you can easily add or substact with each other . For this you have add or substract first element with the first element of second matrix and you have adopt same procedure for others see the photo and understand . You are seeing this picture . This is show that only same order matrices can add or substact .
Main Types of Matrix
Main Types of Matrix
1. Square matrix
Square matrix is a matrix in which number of rows and number of columns are equal .
2. Rectangular matrix
Rectangular matrix is a matrix in which the number of rows and number of columns are not equal.
3. Diagonal matrix
Diagonal matrix is a matrix in which all element is zero except main diagonals.
4. Identity matrix
Identity matrix is a matrix in which all main diagonal are equal
5. unit matrix
Unit matrix is a matrix in which main diagonals are equal to one
6. zero matrix
Zero matrix is matrix in which all elements of matrix are equal to zero.
7. Transpose of matrix
If rows changed into columns and columns changed into rows after this a new matrix comes into existance that is called transpose of matrix.
8. Symmatric matrix
If a matrix and his transpose equal then this matrix is called symmatric matrix
9. Submatrix
If from a big matrix we separate some rows or columns and we make a matrix this is called submatrix .
1. Square matrix
Square matrix is a matrix in which number of rows and number of columns are equal .
2. Rectangular matrix
Rectangular matrix is a matrix in which the number of rows and number of columns are not equal.
3. Diagonal matrix
Diagonal matrix is a matrix in which all element is zero except main diagonals.
4. Identity matrix
Identity matrix is a matrix in which all main diagonal are equal
5. unit matrix
Unit matrix is a matrix in which main diagonals are equal to one
6. zero matrix
Zero matrix is matrix in which all elements of matrix are equal to zero.
7. Transpose of matrix
If rows changed into columns and columns changed into rows after this a new matrix comes into existance that is called transpose of matrix.
8. Symmatric matrix
If a matrix and his transpose equal then this matrix is called symmatric matrix
9. Submatrix
If from a big matrix we separate some rows or columns and we make a matrix this is called submatrix .
Monday, September 1, 2008
What is matrix
Matrix is set of numbers which is bounded by two brackets . Vertical lines is called columns and horizontal lines is called rows . Matrix is always in m X n order . Here m is number of rows and n is numbers of columns
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