Lecture 9: Linear Programming

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Restricted normal form • The constraints can always be written such that – All constraints are written as equalities – Number of constraints M ≤ N – Each constraint equation has a variable that appears in that equation alone (How to do this to be discussed later) • This permits us to obtain a solution via the “simplex method” 201
The simplex method (illustrated by example) • Example (N=4, M=2) Maximize z = – 4x 1 – 25x 2 + 4x 3 + x 4 subject to x 1 + 6x 2 –x 3 = 2 –3x 2 + 4x 3 + x 4 = 8 Move variables that appear in only one constraint equation to the left hand side and call them left hand variables 202
Page 1 and 2: Lecture 9: Linear Programming • A
Page 3 and 4: Linear Programming • The constrai
Page 5 and 6: Feasible vectors • 2-D example: Z
Page 7: Feasible basic vectors The total nu
Page 11 and 12: Solution via the simplex method Rep
Page 13 and 14: Solution via the simplex method We
Page 15 and 16: Solution via the simplex method Set
Page 17 and 18: Keep pivoting until the “z row”
Page 19 and 20: Obtaining the constraints in restri
Page 21 and 22: Treatment of inequalities (Equivale
Page 23 and 24: Getting the constraints into restri
Page 25 and 26: Getting the constraints into restri

Lecture 9: Linear Programming

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