3 Five lecturers were given the following scores when matched against criteria for teaching five courses in a college. Each lecturer is to be allocated to exactly one of the courses so as to maximise the total score of the five lecturers.

1. Explain why the Hungarian algorithm may be used if each number, \(x\), in the table is replaced by \(17 - x\).
2. Form a new table by subtracting each number in the table above from 17. Hence show that, by reducing rows first and then columns, the resulting table of values is as below.

   0	0	3	3	0
   4	3	4	0	2
   0	6	7	2	2
   5	2	3	0	6
   3	1	0	2	0

3. Show that the zeros in the table in part (b) can be covered with two horizontal and two vertical lines. Hence use the Hungarian algorithm to reduce the table to a form where five lines are needed to cover the zeros.
4. Hence find the possible allocations of courses to the five lecturers so that the total score is maximised.
5. State the value of the maximum total score.