So once i am writing this basically what is the job

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constraints. So, once I am writing this basically, what is the job of optimization technique is that, how to find out the solution of this types of model. So, basically through optimization technique, what we will try to learn is that how to maximize or how to minimize a function subject to certain constraints. If you see instead of unit profit I have written here unit profit. If I write down this portion as unit cost as unit cost in that case instead of the maximization problem; obviously, I try to minimize my function and in that case your maximize will be reduced will be replaced by minimize. So, the problem may be maximization problem, the problem may be minimization problem. Depending up on what the data’s are available. So, we want to learn the techniques through which we can solve this kind of problems. Basically, if you see George Dantzig, he developed this optimization; first optimization technique in 1940’s to solve some problems related to military applications. That was the first thing he developed which we call as the linear programming problem. And that was the first optimization technique which was developed at the beginning. After that, lot of optimization models techniques had been developed for solving different types of problems. And these are widely used now a days in operational research, artificial intelligence, computer science and obviously, needless to say in industry it is being widely used. And which is helping a lot to the industry people. Through these optimization techniques, we try to solve various kinds of problems. I can list the problems; one we call as the linear problems. Well, in the linear problems what we say, the optimization function basically should be linear. Whenever, the optimization or function or the constraints are linear functions then those types of problems we call it as the linear functions. Whereas, there is other type of problems, which I call non-linear problems, in non-linear problems whenever the optimization function or the constraints are non-linear in nature then those problems we call it as the non-linear problems.
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We have the other type of problem that is we call it as discrete, in discrete case; what happens, the value of the variable will take some discrete integer values. Just like if you see whenever, I try to find out or made the class time table for teachers and I m locating subject to different rooms always they will takes some integer values. Or, in a hospital whenever, I am giving scheduling duties of the nurses those are taking the discrete values. This kind of problems we call it as the discrete problems. There is another type which we call it as continuous problems, in continuous it can take any value any real value can be taken over there. And in this case; anything whatever you do, it can take 1.5, 1.10 something like this way, any real values it can take. So, we can categorize our problems linear, non-linear, discrete and continuous. And for each type of problem we have several different optimization techniques. We will go through one by one all these things.
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