3 In the London 2012 Olympics, the Jamaican \(4 \times 100\) metres relay team set a world record time of 36.84 seconds.
Athletes take different times to run each of the four legs.
The coach of a national athletics team has five athletes available for a major championship. The lowest times that the five athletes take to cover each of the four legs is given in the table below.
The coach is to allocate a different athlete from the five available athletes, \(A , B , C , D\) and \(E\), to each of the four legs to produce the lowest total time.
| Leg 1 | Leg 2 | Leg 3 | Leg 4 |
| Athlete \(\boldsymbol { A }\) | 9.84 | 8.91 | 8.98 | 8.70 |
| Athlete \(\boldsymbol { B }\) | 10.28 | 9.06 | 9.24 | 9.05 |
| Athlete \(\boldsymbol { C }\) | 10.31 | 9.11 | 9.22 | 9.18 |
| Athlete \(\boldsymbol { D }\) | 10.04 | 9.07 | 9.19 | 9.01 |
| Athlete \(\boldsymbol { E }\) | 9.91 | 8.95 | 9.09 | 8.74 |
Use the Hungarian algorithm, by reducing the columns first, to assign an athlete to each leg so that the total time of the four athletes is minimised.
State the allocation of the athletes to the four legs and the total time.
[0pt]
[11 marks]
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