Question: Let a , c R n be two vectors and b R be a number. Consider the linear programming problem (LPP): minimize c T x

Let a,cRn be two vectors and bR be a number. Consider the linear programming problem (LPP):

minimizecTx

subjectto:aTx=b

Suppose x0H:={xRn:aTx=b} is a solution to this LPP. Prove that c is perpendicular to the hyperplane H. That is, show that cT(x0x)=0.

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