MAS 801 It's a Discreetly Discrete World Ã¢Â€Â“ Mathematics in Real-life ...

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Lecture 9: 22 October 2008 Proving Optimality: Method of Tight Restrictions • For simple 2-variable LPs, we have seen how the graphical method can be used to find the optimal solution rather easily • To prove that the answer obtained by the graphical method is actually optimal, we need more than just drawing diagrams • For example, we have obtained (x,y) = (100,100) as the optimal solution to the LP maximize z = 1000x + 3000y subject to x + 2y ≤ 300 x + 5y ≤ 600 x ≥ 0 y ≥ 0 • How do we know (100,100) is really the optimal solution
Lecture 9: 22 October 2008 Proving Optimality: Method of Tight Restrictions • What does it take to show that (x,y) is really an optimal solution • We need to show two things: • That (x,y) is a feasible solution • No other feasible solution gives a better objective function value • To show that (x,y) is a feasible solution is easy • Just plug the values of x and y into the constraints and show that they are all satisfied • To show the second is harder
Page 1: Lecture 9: 22 October 2008 MAS 801
Page 5 and 6: Lecture 9: 22 October 2008 Proving
Page 7 and 8: Lecture 9: 22 October 2008 Exercise
Page 9 and 10: The Mathematics of Lecture 9: 22 Oc
Page 11 and 12: Lecture 9: 22 October 2008 How Big
Page 13 and 14: How Big is the Web (Graph) Lecture
Page 15 and 16: Lecture 9: 22 October 2008 Overview
Page 17 and 18: Lecture 9: 22 October 2008 Indexer
Page 19 and 20: Lecture 9: 22 October 2008 Ranking
Page 21 and 22: Lecture 9: 22 October 2008 PageRank
Page 23 and 24: Lecture 9: 22 October 2008 Adjacenc
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Page 41 and 42: Lecture 9: 22 October 2008 Eigenval
Page 43 and 44: Lecture 9: 22 October 2008 Eigenval

MAS 801 It's a Discreetly Discrete World Ã¢Â€Â“ Mathematics in Real-life ...

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