Lecture 9: Linear Programming

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Treatment of inequalities • Convert all inequalities according to this prescription – This increases the dimensionality of the problem from N to N + K, where K is the number of inequalities – Solve by the previous method – Ignore the solution for the y j 215
Getting the constraints into restricted normal form Arranging for every constraint equation to have a variable that appears in that equation alone Change the constraint equations into “zero form”: Define z j ≡ ∑ c ij x i – b j N i= 1 The original M constraints become z j = 0 216
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 and 18: Keep pivoting until the “z row”
Page 19 and 20: Obtaining the constraints in restri
Page 21: Treatment of inequalities (Equivale
Page 25 and 26: Getting the constraints into restri

Lecture 9: Linear Programming

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