Transcription of Chapter 7
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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. Ifsomevariablexjisunrestrictedinsign,rep laceiteverywhereintheformulationbyx0j x00j,wherex0j 0andx00j 2x1+3x2x1 3x2+2x3 3 x1+2x2 2x1urs;x2 0;x3 0 Letus 3x2x1 3x2+2x3+s1=3 x1+2x2 s2=2x1urs;x2 0;x3 0s1 0s2 0 Thelaststepistoconverttheunrestrictedvar iablex1intotwononnegativevariables:x1=x0 1 2x001 3x2x01 x001 3x2+2x3+s1=3 x01+x001+2x2 s2=2x01 0;x001 0;x2 0;x3 0s1 0s2 ,inthiscoursewesolve\byhand"onlythecasew heretheconst
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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THE SIMPLEX METHOD, Linear programming, Method, MATHEMATICS UNIT 1: REAL ANALYSIS, PROGRAMMING, Simplex method, 4 The Simplex Method and the Standard, 4 The Simplex Method and the Standard Minimization Problem, Software for Large-Scale Nonlinear Programming, 4 UNIT FOUR: Transportation and Assignment, 4 UNIT FOUR: Transportation and Assignment problems 4, 9.1 Strictly Determined Games, Approaches to Capacity Planning, Business Analytics Principles, Concepts, and, Business Analytics Principles, Concepts, and Applications