Note: if you cannot remember how to represent matching problems in graphs and matrices, revise notes for 6.1 Introduction to Matching Problems.

### Optimum Assignment by Inspection

- In smaller scale matching problems, it may be possible to determine the optimum assignment by inspection.
- One method is to find the lowest weight assignment for each task, object, etc. being assigned to. If there is any conflict, then consider other tasks, objects, etc.

Example

Teacher |
Banjo |
Violin |
Piano |

Dave |
10 |
25 |
35 |

Jill |
11 |
15 |
40 |

Steve |
10 |
18 |
46 |

Above is a matrix representing the time in days required for each teacher at a school to teach a beginner’s course in certain instruments. Only one teacher is required for each course and each teacher must be assigned to a course. As this is a smaller-scale problem, we will use inspection to find the optimum assignment.