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Chapter 7

Chapter7 TheSimplexMethodInthischapter, ,youwillbeabletoidentifywhenaproblemhasa lternateoptimalsolutions(SOLVER nevertellsyouthis:italwaysgiveyouonlyone optimalsolution). ,wepointoutthateverylinearprogramcanbeco nvertedinto\standard"formMaxc1x1+c2x2+:: :+cnxnsubjecttoa11x1+a12x2+:::+a1nxn=b1: ::::::::am1x1+am2x2+:::+amnxn=bmx1 0;:::xn 0wheretheobjectiveismaximized, : Iftheproblemisminz,convertittomax z. Ifaconstraintisai1x1+ai2x2+:::+ainxn bi, +ai2x2+:::+ainxn+si=bi,wheresi 0. Ifaconstraintisai1x1+ai2x2+:::+ainxn bi, +ai2x2+:::+ainxn si=bi,wheresi 0.

Chapter 7 The Simplex Metho d In this c hapter, y ou will learn ho w to solv e linear programs. This will giv ey ou insigh ts in to what SOL VER and other commercial linear programming soft

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