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

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Exercise 1 • Solve the LP from Exercise 4 by examining the extreme points of the feasible region maximize z = 2000x + 3000y subject to x + y ≤ 15 3y ≤ x x ≥ 0 y ≥ 0
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
Page 1 and 2: MAS 801 It’s a Discreetly Discret
Page 3: Extreme Points • The following is
Page 7 and 8: Proving Optimality: Method of Tight
Page 9 and 10: Proving Optimality: Method of Tight
Page 11 and 12: Tight Inequalities • An inequalit
Page 13 and 14: The Web Graph • Primary focus is
Page 15 and 16: How Big is the Web (Graph)
Page 17 and 18: Searching the Web • We have seen
Page 19 and 20: Crawler • Program that browses WW
Page 21 and 22: Query Engine • When given input k
Page 23 and 24: PageRank • Assigns a rank to ever
Page 25 and 26: PageRank: First Try • We want to
Page 27 and 28: Adjacency Matrix of a Digraph • E
Page 29 and 30: Matrix Transpose Matrix Transpose
Page 31 and 32: Exercise 2 • Compute the importan
Page 33 and 34: PageRank: An Improvement • The pr
Page 35 and 36: Markov Matrix of a Digraph • Exam
Page 37 and 38: Exercise 3: Answer 1 2 3 4 5 6 •
Page 39 and 40: Exercise 4 • Compute the importan
Page 41 and 42: PageRank: An Improvement • The pr
Page 43 and 44: Some Linear Algebra • Given an n
Page 45 and 46: Exercise 5 • Find the eigenvalues
Page 47 and 48: Example • Find all the eigenvecto
Page 49: Further Properties of Matrices •

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

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