5. The manager of a car hire firm has to arrange to move cars from three garages \(A , B\) and \(C\) to three airports \(D , E\) and \(F\) so that customers can collect them. The table below shows the transportation cost of moving one car from each garage to each airport. It also shows the number of cars available in each garage and the number of cars required at each airport. The total number of cars available is equal to the total number required.
| Airport \(D\) | Airport \(E\) | Airport \(F\) | Cars available |
| Garage \(A\) | £20 | £40 | £10 | 6 |
| Garage \(B\) | £20 | £30 | £40 | 5 |
| Garage C | £10 | £20 | £30 | 8 |
| Cars required | 6 | 9 | 4 | |
- Use the North-West corner rule to obtain a possible pattern of distribution and find its cost.
(3) - Calculate shadow costs for this pattern and hence obtain improvement indices for each route.
- Use the stepping-stone method to obtain an optimal solution and state its cost.