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Where do you run into a real world situation involving 3 variables and 3 equations? Can someone think of a specific example from business, etc? I recall taking an operations research course that seemed to involve optimization of 3 variables, but do not recall a single example or theme. Any help is appreciated.

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If you are wondering if a model with 3 variables seems like overkill, you should consider that "real world situations" involve a HUGE number of variables, but they are typically assumed to be constant for the sake of a manageable model. –  MPW Mar 31 at 17:57

2 Answers 2

A few examples that may or may not arise in other answers...

  • When you have a set of data of the form $(x_i,y_i,z_i)$ and you want to fit a model of the form

$$z=a\,f(x,y)+b\,g(x,y)+c,$$

least squares leaves you with three equations in $a$, $b$ and $c$.

  • Any kind of a 'network flow'. For example suppose that you have a roundabout with three exits and the flow in and out of each exit is known then using the principle that the flow into a junction should equal the flow out leaves you with three equations in the unknown flow between exists.

  • When doing a partial fraction expansion --- which occurs in various applications --- you are often left with simultaneous equations.

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Linear programming. look HERE ... in fact the first example (rabbit food) involves three variables.

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