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 sippindatbong June 5th, 2015 09:17 PM

Quickest Trick of Linear Programming

So after graphing the constraints, when you get the feasible region, is there a quick trick to checking the appropriate vertex point instead of plugging in and checking? My teacher said something about y=k-x and using it kind of like the Vertical Line Test, but I'm not sure if this works and why, if it does, works.

 Country Boy June 6th, 2015 04:34 AM

In "linear programming" we can think of the object function as a line moving parallel to itself ("ax+ by= constant" is a straight line. That "constant" changing gives parallel lines). As that line moves out of the "feasible area", the last point it touches will be a vertex. If you graph your object function for some constant, you can get an idea which vertex that will be. Perhaps that is what your teacher was referring to.

It might be even quicker to calculate the line perpendicular to the object function line. A line perpendicular to ax+ by= constant is bx- ay= constant.

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