3. To raise money for charity it is decided to hold a Teddy Bear making competition. Teams of four compete against each other to make 20 Teddy Bears as quickly as possible.
There are four stages: first cutting, then stitching, then filling and finally dressing.
Each team member can only work on one stage during the competition. As soon as a stage is completed on each Teddy Bear the work is passed immediately to the next team member.
The table shows the time, in seconds, taken to complete each stage of the work on one Teddy Bear by the members \(A , B , C\) and \(D\) of one of the teams.
| cutting | stitching | filling | dressing |
| \(A\) | 66 | 101 | 85 | 36 |
| \(B\) | 66 | 98 | 74 | 38 |
| \(C\) | 63 | 97 | 71 | 34 |
| \(D\) | 67 | 102 | 78 | 35 |
- Use the Hungarian algorithm, reducing rows first, to obtain an allocation that minimises the time taken by this team to produce one Teddy Bear. You must make your method clear and show the table after each iteration.
- State the minimum time it will take this team to produce one Teddy Bear.
Using the allocation found in (a),
- calculate the minimum total time this team will take to complete 20 Teddy Bears. You should make your reasoning clear and state your answer in minutes and seconds.
(Total 13 marks)