Lecture 9: Linear Programming

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Generalization to N variables and M constraints • The maximum number of required pivots is min(N – M, M) • The process can (and should) fail if there are no negative entries in a column headed by a positive pivot – implies there is no maximum allowed value of z (i.e. no boundary prevents us from going to infinity along that basis vector) 211
Obtaining the constraints in restricted normal form • What happens if – Some constraints are inequalities – Not every constraint equation has a variable that appears in that equation alone – Number of constraints M > N • General solution: increase the number of variables! 212
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 and 8: Feasible basic vectors The total nu
Page 9 and 10: The simplex method (illustrated by
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: Keep pivoting until the “z row”
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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