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You know, in real life, you can model a lot...in linear algebra form. For example, equations and matrices and so on and so forth really lay out the foundation for you to understand and translate a business problem into a mathematical model.
You can model it as a linear equation and...putting a certain constraint on it, and you try to find a mathematical solution, and this is called optimization problem in the transportation industry. And you can use that in many, many industries.
For example, when you have a lot of calls getting to your telecommunication network, how do you route those calls to different parts of the country, so you know, you don't have to build a huge amount of capacity to accommodate those calls.
But in the overall game, the fundamental problem is a mathematical problem, and by learning certain mathematical skills, it will enable you to understand those problems and to find a solution for that...by looking for, say, all the possible routes between two points and then looking for ways of programming the system so that the most efficient route is taken in any given case...and then you kind of allocate resources.
You know, one of the technical problems in mathematics and especially operations research people face is called shortest path problem. It's basically--you can build a network from point A to point B and a network means that you from this point A, you can travel to different point and then finally get travel to another point and finally get to point B. So you traverse many, many points in this network....The time is not only dependent on distance, but also on the [demand]...The idea is that in order to send a certain amount of messages from point A to point B, you have to travel different routes. What is the minimum cost or the minimum capacity needed on this network to allow you to transfer those messages from A to B and ask, well, or build a mathematical model and figure out what is the minimum capacity needed to do that?
And you can use linear algebra ideas to, you know, you have the object function that you can model as a linear object function allowing certain constraints. For example, you cannot have more than 20 calls on this line. And it's also, you know, from there to here you can model it as a linear equation which says, you know, the call on this line has less or equal to 20. And another line may be less or equal to 10 or maybe because there's costs, what have you, a certain line you have to be minimum to carry a certain amount of calls--maybe you say greater or equal to 10 or whatever. You can pull those equations together and so you have an objective and you have a list of constraints and that's kind of...a mathematical model for you to solve.
[The shortest path problem] is a particular type of optimization problem...and then you can generalize it, it becomes a transportation problem. You can have a [telecommunications] network problem, a different sort of problem that utilizes that same concept but is just a little bit more complex problem to solve.
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