3. Jameson cars are made in two factories A and B. Sales have been made at the two main showrooms in London and Edinburgh. Cars are to be transported from the factories to the showrooms. The table below shows the cost, in pounds, of transporting one car from each factory to each showroom. It also shows the number of cars available at each factory and the number required at each showroom.
| London (L) | Edinburgh (E) | Supply |
| A | 80 | 70 | 55 |
| B | 60 | 50 | 45 |
| Demand | 35 | 60 | |
It is decided to use the transportation algorithm to obtain a minimal cost solution.
- Explain why it is necessary to add a dummy demand point.
- Complete the table below.
| L | E | Dummy | Supply |
| A | 80 | 70 | | 55 |
| B | 60 | 50 | | 45 |
| Demand | 35 | 60 | | 100 |
- Use the north-west corner rule to obtain a possible pattern of distribution.
(1) - Taking the most negative improvement index to indicate the entering square, use the stepping-stone method to obtain an optimal solution. You must make your shadow costs and improvement indices clear and demonstrate that your solution is optimal.
(7) - State the cost of your optimal solution.
(1) (Total 13 marks)