In a quiz there are four individual rounds, Art, Literature, Music and Science. A team consists of four people, Donna, Hannah, Kerwin and Thomas. Each of four rounds must be answered by a different team member. The table shows the number of points that each team member is likely to get on each individual round.
\cline { 2 - 5 }
\multicolumn{1}{c|}{}
Art
Literature
Music
Science
Donna
31
24
32
35
Hannah
16
10
19
22
Kerwin
19
14
20
21
Thomas
18
15
21
23
Use the Hungarian algorithm, reducing rows first, to obtain an allocation which maximises the total points likely to be scored in the four rounds. You must make your method clear and show the table after each stage.
(Total 9 marks)