Question: For some matrix A ( Rmxa and some vector b ( R, consider the Linear Program (P): max (503 : Ar = b, x 2

For some matrix A ( Rmxa and some vector b ( R", consider the Linear Program (P): max (503 : Ar = b, x 2 0) (note that the objective is always a constant). Below, (D) denotes the dual of (P). (a) Prove that (D) is feasible (for all A, b). (b) If (P) is infeasible, prove that (D) admits a solution of value -2016. (c) Explain how (b) above is related to Proposition 2.1 of your textbook. PROPOSITION 21 Led A be a matrix and b be a vector, Then the system Ar-b 120 has no solution if there exists a vecdory such that (1) JAzO. and () y b

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