Lecture 9: Linear Programming

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The fundamental theorem of linear programming “If an optimal feasible vector exists, then there is a feasible basic vector that is optimal” i.e. the optimal vector is at one of the vertices Our goal is to find which vertex (i.e. which N of the constraints does it satisfy) 199
Feasible basic vectors The total number of locations at which N constraints are satisfied simultaneously can be very large: It can be as large as the number of ways of choose N items out of N+M, which comes to (N+M)! / (N! M!) In the 2-D example, N=2, M=3, and so (N+M)! / (N! M!) = 5!/(3!2!) = 10 of which 5 lie in the feasible space and one is missing (since x 1 =0 and x 1 =3 cannot be satisfied simultaneously) 200
Page 1 and 2: Lecture 9: Linear Programming • A
Page 3 and 4: Linear Programming • The constrai
Page 5: Feasible vectors • 2-D example: Z
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 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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