- Four students, \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D , are to be allocated to four rounds, \(1,2,3\) and 4 , in a competition. Each student is to take part in exactly one round and no two students may play in the same round.
Each student has been given an estimated score for each round. The estimated scores for each student are shown in the table below.
| \cline { 2 - 5 }
\multicolumn{1}{c|}{} | 1 | 2 | 3 | 4 |
| A | 34 | 20 | 18 | 15 |
| B | 49 | 31 | 12 | 34 |
| C | 48 | 27 | 23 | 26 |
| D | 52 | 45 | 42 | 42 |
- Reducing rows first, use the Hungarian algorithm to obtain an allocation that maximises the total estimated score. You must make your method clear and show the table after each stage.
- Find this total estimated score.