## Edexcel AS and A Level Modular Mathematics Decision Mathematics 2 D2

(2016)

### Abstract

Edexcel's own course for the 2008 specification. Providing the best possible match to the specification, Edexcel AS and A Level Modular Mathematics DM2 motivates students by making maths easier to learn.

Completely re-written by chief examiners for the specification, it provides student-friendly worked examples and solutions, leading up to a wealth of practice questions. Sample past exam papers for thorough exam preparation, and regular review sections that help consolidate learning are included. Opportunities for stretch and challenge are presented throughout the course.

Also included is an interactive FREE LiveText CD-ROM, containing Solutionbank and Exam Cafe to support and inspire students to reach their potential for exam success. Solutionbank contains fully worked solutions with hints and tips for every question in the Student Book. Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with chief examiner's commentary.

Section Title Page Action Price
Cover Cover
Contents ii
Chapter 1: Transportation problems 1
1.1: Terminology used in describing and modelling the transportation problem 2
1.2: Finding an initial solution to the transportation problem 3
1.3: Adapting the algorithm to deal with unbalanced transportation problems 6
1.4: Knowing what is meant by a degenerate solution and how to manage such solutions 7
1.5: Finding shadow costs 10
1.6: Finding improvement indices and using these to find entering cells 15
1.7: Using the stepping-stone method to obtain an improved solution 17
1.8: Formulating a transport problem as a linear programming problem 26
Summary of key points 31
Chapter 2: Allocation (assignment) problems 32
2.1: Reducing cost matrices 33
2.2: Using the Hungarian algorithm to find a least cost allocation 34
2.3: Adapting the algorithm to use a dummy location 43
2.4: Adapting the algorithm to manage incomplete data 44
2.5: Modifying the algorithm to deal with a maximum profit allocation 48
2.6: Formulating allocation problems as linear programming problems 52
Summary of key points 59
Chapter 3: The travelling salesman problem 61
3.1: Understanding the terminology used 62
3.2: Knowing the difference between the classical and practical problems 62
3.3: Converting a network into a complete network of least distances 62
3.4: Using a minimum spanning tree method to find an upper bound 67
3.5: Using a minimum spanning tree method to find a lower bound 73
3.6: Using the nearest neighbour algorithm to find an upper bound 78
Summary of key points 86
Chapter 4: Further linear programming 88
4.1: Formulating problems as linear programming problems 89
4.2: Formulating problems as linear programming problems, using slack variables 91
4.3: Understanding the simplex algorithm to solve maximising linear programming problems 94
4.4: Solving maximising linear programming problems using simplex tableaux 101
4.5: Using the simplex tableau method to solve maximising linear programming problems requiring integer solutions 114
Summary of key points 120
Review Exercise 1 121
Chapter 5: Game theory 134
5.1: Knowing about two-person games and pay-off matrices 135
5.2: Understanding what is meant by play safe strategies 136
5.3: Understanding what is meant by a zero-sum game 137
5.4: Determining the play safe strategy for each player 137
5.5: Understanding what is meant by a stable solution (saddle point) 138
5.6: Reducing a pay-off matrix using dominance arguments 144
5.7: Determining the optimal mixed strategy for a game with no stable solution 145
5.8: Determining the optimal mixed strategy for the player with two choices in a 2*3 or 3*2 game 149
5.9: Determining the optimal mixed strategy for the player with three choices in a 2*3 or 3*2 game 153
5.10: Converting 2*3, 3*2 and 3*3 games into linear programming problems 153
Summary of key points 164
Chapter 6: Network flows 165
6.1: Knowing some of the terminology used in analysing flows through networks 166
6.2: Understanding what is meant by a cut 171
6.3: Finding an initial flow through a capacitated directed network 178
6.4: Using the labelling procedure to find flow-augmenting routes to increase the flow through the network 182
6.5: Confirming that a flow is maximal using the maximum flow minimum cut theorem 193
6.6 Adapting the algorithm to deal with networks with multiple sources and/or sinks 197
Summary of key points 205
Chapter 7: Dynamic programming 207
7.1 Understanding the terminology and principles of dynamic programming, including Bellmanâ€™s principle of optimality 208
7.2 Using dynamic programming to solve maximum and minimum problems, presented in network form 209
7.3 Using dynamic programming to solve minimax and maximin problems, presented in network form 217
7.4 Using dynamic programming to solve maximum, minimum, minimax or maximin problems, presented in table form 221
Summary of key points 232
Review Exercise 2 233
Examination style paper 241