This looks a lot like a problem from Linear Programming like e.g. the Simplex Algorithm
How? How can the equations I provided be transformed as input to the simplex algorithm (s.a.)? Are there any other objectives other than maximimze or minimize with s.a.? As I don't need either. Also, what happens with s.a. when number of equations is less than Ndim?
One day I was contemplating about different supermarkets having different prices for same products and asked "for X money where do you buy more olives and less fetta?" | [reply]
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> "for X money where do you buy more olives and less fetta?"
By which criteria ???
Trivially you buy feta in the cheapest supermarket F and olives in the cheapest O ...
Or do you say going to multiple supermarkets isn't practical and you want to minimize the costs for time and fuel?
Or do you say you need a minimum amount f of feta and o of olives and you need the supermarket where you can buy the whole package to the best condition?
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I guess the last one. Mainly from the point of view of discovering some kind of supermarket price policy (someone claimed that one day olives are up and fetta down, then the other day the opposite happen. you can replace fetta+olives with salt+pepper, tomato+cucumber, chicken+noodles and on to bigger groups, etc.etc.
Anyway, the interesting question is what you asked: can the intersection of M hyperplanes in N dimensions be solved as a linear algebra problem, perhaps by the simplex algorithm. Will it be faster?
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