Hello students , myself Dr. Gajendra Purohit and I have done my Phd in algebra and students CSIR exam has been cleared by me and I upload the videos for engineering mathematics and bsc students and many students face problems as many students ask where are certain videos so if you are facing any problem the playlist here made over here is for your reference as I have made different playlist so you can go there and see the videos and if you are facing any problem then then you can go to the comment box and comment and students there might be some small plus minus mistakes you can go and comment there so that I can rectify those mistakes and where there is pin comment I am going to update over there also so that you know where I have done the mistake and you avoid the same and students if you are preparing for CSIR-NET then you can go to the playstore and download the unacademy app and search Gajendra Purohit and then follow me there so that whatever are my courses you can get a notification for all of them and do read,review my course and share among your friends so that they can also get the benefit of thsi Hello students myself Dr. Gajendra Purohit and today I will start operation research and some related topics and in these only I will the topic of statistics as under operation research some parts of statistics are there like distribution and random variable concept and then some basic concepts under probability like moment MGF and CF so these I will discuss in front of you all but for now the linear programming problem is what I am going to start and I want to tell you that for operation research I am going to cover all these topics under which first I take I will linear programming problem and to solve this we have many methods like first we have the graphical method the we have the simplex method then big M method then we have revise simplex method concept so that all we will discuss here then we have unity concept that also I will discuss in front of you and after that we have the concept of transportation in which we solve transportation problem with different methods like north east corner method and minimum cost method and even more and there are more tests of optimality which are applied like here we have VAM method that is vogel's approximation method that also we will discuss here then we have assignment model that also I will take in front of you all let me give you some idea that this operation research and business related problems is made ultimately here we have to understand that any business model works on two concepts first is that our profit should be maximized and our cost should be minimum plus the resources which are available to us we have to make the optimum use of it Now we will study that how can we make use of resources like similar happens in transportation like you have a location and from different locations you have to send the crane on that particular location. So which crane we have to send first and how we will send so that your transportation cost should come minimum and you have godowns and warehouses and you have to shift the material so where to place which material so that your transportation cost is minimum then under assignment problem model we have like you do four works and you have to give work to four people and for everyone's cost you know that this person takes this much and that person takes that much So which work you have to assign to whom So that comes in assignment problem and then dynamic programming is also a very important concept The idea of dynamic programming is that here the products that get easily damaged like if we talk about pastry or flower business or newspaper like now a days newspaper is of no use. Right? So in business like this the problems faced can be solved by dynamic programming very easily like if we talk about pastry and if i have opened my bakery so how much pastries i have to make everyday so that it does not get wasted. So this we will discuss here then we have game theory and it is also a very good model and on this also we solve many problems. Normally this is probability based So this is also i will discuss in front of you. Now next is queuing theory and this is also very important like we have different models like capacity based like single server model then finite capacity, single server or infinite capacity multi server finite capacity, multi server infinite capacity. So these different models I will discuss in front of you. Then next is PERT/CPM. So project evolution techniques and critical path method so if we are given a project and it's path is given and you have to do this work in this much time and so on so at the end which path we have to use by seeing this so that we invest less time and cost is also less that also I will discuss with you all. After that we have inventory model students inventory model is very helpful and this comes even in exams and in real life also it is used a lot as if there is any business , the main problem that comes is of stock that ho much stock should we keep. Right? so based on that also we have yoke model and we will discuss that also. There are two types of model deterministic and probabilistic model that we will discuss after that we have monte-carlo stimulation method and this is also a very good method and a lot of questions are asked in the exams on operation research. Then comes the last topic that is sequencing which is known as chop sequencing that for which machine it is , two machine there is two machine n job and n machine n job plus graphical method and even three machine n job is also there and n machine n job type of questions we solve graph for them so that I will discuss here. So students first we will see what is linear programming problem so linear word itself tells that the x would be that whatever the equation will be it's degree will be one now what happens is that in linear programming problem let me tell you that the videos on youtube that we upload for you. Right? So i see the comments of the students that sir please the proof of green theorem or proof of this theorem or proof of that theorem. So what we teach you on youtube in that we tell you the concepts and numericals based on them. Right? If we go deep into the theory then we do not have much time and for proving one theorem, around 8-10 minutes are wasted. If I go and prove the theorem then my lot of time is wasted . You can easily understand the proof from the textbook If you have understood the numerical concept and its applications so then if you understand the proof you won't get any problem. Right? The content which we are bringing for you on youtube, students we want to guide you, we want to go through the subject that this subject is this. Right? If you wish that on operation research the book that we have like Hira Gupta or S K Bhambri...sorry there is one more book, I think of Sharma Sir you please solve the complete book. This is not possible for us If i start solving the book, it will take two years then even I have to upload the video then also in two years I won't be able to solve the book. So students this much is not possible and whatever we are working for you that is just to guide you and make you understand the concept and we solve questions like this if you go through one subject then so while doing questions you won't face any problem. Right? so please keep the expectation that much only that we can help you as more expectation makes us worried as students on my whatsapp daily around 100-175 students send me the questions that sir please solve the questions for us students I don't have this much time . If I solve questions for 100 students then 1 question so it takes around 2-3 minutes to solve questions for one student so around 300-400 minutes will be taken to solve your problems that is around 5-6 hours then how will I upload videos for you all as when I make video I have to look for the content also that what type of content should I bring for you all so that in less time I can explain you more students there are many videos on youtube and many teachers are uploading best videos but the difference between my video and other videos is that in less time I try to explain most of the part and many students have the problem and they say to slow down the speed students in youtube there is a setting if you reduce my speed to 1.5 or 1.75 t will slow down right? If any teacher teaches slowly if we see any video there is a setting option at the top with which we can increase and decrease the speed. If you think my speed is fast then you can go the setting and slow the speed or may pause the video and understand as in today's time and even students don't have much time as in less time we have to give you the maximum so that's why I go this fast so please try to understand our intentions so see here what is linear programming problem if there is any business, in that business our objective is of profit maximization or cost minimization. Right? so here in linear programming problem in that its model first we have the objective function maybe it will be maximum z or it would be given minimum.right? so these two types of problem we have. Right? like if I say you x+2y. right? or it may be given 2x+3y. right? so this is our objective function now if there is any business we have some shortcomings like if I am doing a business so I have this much man power this much money I can do this much work in this much time. right? or if I have this much land available that I can do the work on this much land so our resources are limited. so the resources which we connect with the business model that is called the constraint which we always right in less than greater than form like if I say so this is your objective function and these are the business shortcomings that you have so this is called the constraint. Right? and then whatever resources are there they all are positive like if I say that I have this much money so the money will be positive and if I have this much time so the time will also be positive so this model is called as LPP that is linear programming problem so I want to make you understand that in linear programming problem we have two things one is objective function second is constraint. Right? which means our shortcomings that only this much is available to us which is that we have only this much available for more than that or atleast or atmost or whatever is the requirement demand,supply or whatever is written in this form and in 12th class there is a chapter LPP where we study formation for LPP so you might have studied there but still I will discuss here some of it that how we solve these types of problem with the graphical method then I will tell you how we do the formulation then I will talk about these types of problem with how we solve them with simplex method then we will talk about big M and then two phase and then we will finish this. So students here I have given you the overview of LPP plus what I will teach in operation research that I have told you so the next videos that I will take the next video that is coming will be how with graphical method we solve the linear programming problem and here comes a concept like infinite solution, degeneracy then unmodit solution, no solution or unique solution so these cases I will discuss in my next video. So students thank you so much for watching my videos and if you are liking my videos then please do subscribe to my channel and press the notification bell and students do comment and like as these things motivate a lot that our content is helping you so please don't keep your feeling inside and if you will write in message form so we will understand but if you keep inside we won't get it that how much