 I am Dr. Keshav Valasi from Mechanical Engineering Department of Valgen Institute of Technology, Solapur. In today's session we will briefly discuss about what is the linear programming problem which is in short called as LPP. So, introduction to LPP is our today's topic. At the end of this session students will be able to understand the basic concepts of linear programming problems as well as its applications. Now what is LPP? Is basically a mathematical tool or a technique for the optimization of consumption of different resources in any business. What I mean by any business it could be manufacturing or service type of business and in any business we have different types of resources and how can we best optimally use these resources. The answer to this can be taken up probably with this LPP and why LPP is all the relationships that we have here they are linear in nature. So it is called as a linear programming problems. Now main features if we talk for LPP the very first is the variables in the problem. What are the situation we are thinking of in any business for applying this LPP there we need to really focus on the types of variables. It is particularly the time unit again and defining these variables precisely is the most fundamental aspect in the formulation of LPP problem. If you go wrong in defining variables the problem will be wrong and the solution will be wrong. So the very first care we have to take is the variables in the problem must be defined very much correctly. Second is objective function. Now this objective function is something that we want to achieve in the business. For example if something is on profit side or income side or revenue side if you are thinking of some parameters like this naturally we would aim at increasing that we would aim at maximizing that that is we would aim at maximizing profit revenue income or sales types of parameters. And if it is cost related thing or distance related thing or time related thing such parameters then probably we would aim at minimizing these parameters that is minimizing total cost minimizing distance or time such parameters. So what we are aiming at based on that we have to define our objective function. And third main feature in LPP is the constraints. These constraints are nothing but the basic restrictions or limitations as we have said earlier also. In any business we have got lots of resources consumed man, machine, material, money and even some data could be from market research also. Now these all resources they put some limitations what I mean is in any business naturally we have some restrictions on the money it is never so like you demand any money it can be poured in any business no we have limitations. So such limitations are referred as restrictions or in LPP language they are particularly called as constraints. Even for example you can have manpower then suppose you have got 10 workers then one worker is working for 8 hours a shift. So 10 workers we have got 80 hours per day. So in a day we are having only 80 hours time from the workers. So this becomes the limitation 80 hours means we do not have 90 hours so conversely seen in that. That is the restriction we our working cannot go beyond 80 hours of consumption of man hours that is the meaning of constraints. So these are the three main features different variables of the problem objective function that is something to be achieved and constraints that is the limitations of the problem. At this point I would expect you all people to just try to apply these concepts given here as main features try to apply these concepts to some application area some domain you can think of some industry or nation or maybe service industry or whatever you think of some environment you think of and how can you think of applying that in those situation applied mind is very important for these types of techniques to be really implemented or used in any situation. Now here as we have discussed all the variables that we define in the problem they are used in formulating the objective function as well as the constraints. Some mathematical relationship between these variables and the resources we establish that all these relationships all these mathematical relationships of the variables considering these different resources these mathematical relationships are linear in nature. Now what I mean by linear in nature their degree of polynomial is 1 and hence looking to this particular linear relationship of these all variables it is referred as linear programming problems. Next is in some books if you see they have said war is an art as well as science. Now as far as the mathematical formulation is concerned there you are collecting the data more convincingly I would take the example of again a market research. Now the data that we collect from market research say if you take two different consultants two different teams working on the same problem then the findings of the data from the market by two teams two consultants will be different. So their experiences how many years they have the experience in this field their skills their intelligence level their abilities to handle the data so many parameters human aspect comes into picture. And hence the extent to which that skill aspect human aspect comes in picture collecting the data that we call as an art because if the data that you collect from market research say for example if that is wrong one example we are taking as a market research what forecasting technique you are raising what questionnaire you are raising what sample size you are taking which audience which people you are contacting for the information these all things they reflect on the data collected and hence two persons will have different data two persons will have different skills different abilities to formulate to that extent it is an art. But once you take up a particular mathematical set of a model of these relationships then for that mathematical model maths being a science mathematics is the perfect science hence for a particular model a particular mathematical set of relationships that we come up with the solution has to be unique across the globe and in that sense it is a science. Next is here this LPP is applied in almost any field you can just take we will just talk of some fields here one example we will talk is a manufacturing industries say here you may think of some automobile industry and in that industry in previous video those we have seen we discussed how the methodology is used. So different types of models of the vehicles you can use the data to formulate the objective function as well as you can use the data to formulate the constraints also and it can be done for any manufacturing industry why only automobile you can do it for laptop manufacturing company mobile manufacturing company sugar cement any any industry chemical textile for any industry you can think of applying this linear programming problem by formulating certain objective function and a set of constraints based on the variables from given situation we can apply it to any service sector or software industry also for example in software industry say we have got Infosys or Cognizant similar we prove so many organizations we have these are all service industries so there also we can think of applying linear programming problems so as to optimize the consumption of resources you have got so many computers in these organizations and how best you can apply you know resource consumption particularly if we just go little at micro level then overseas projects what these software industries are having their timings of the shifts are very odd seen in Indian timing IST what we call and there you can really optimize the using of these resources different laptops and hardware and communication medias that they have in all to interact with their customers overseas or maybe in India also so there also you can use it for the optimum utilization of their resources which could be man or other equipments in agricultural yes you can utilize for crop optimization multiple crops how can you take it and gets the best get the best output get the best yield same in the medical field we have the applications in optimizing the resources or services of medical practitioners in the military ISRO NASA yeah satellite launching kinds of things lots of applications are there in finance in banking LIC different types of investments how can you optimize your variety of investments you can utilize there so LPP has got tremendous applications these are the three books Taha Sharma and Gupta and additional resources you can definitely use thank you