5. The table below shows the cost of transporting one unit of stock from each of four supply points, 1 , 2,3 and 4, to each of three demand points, A, B and C. It also shows the stock held at each supply point and the stock required at each demand point. A minimal cost solution is required.
| A | B | C | Supply |
| 1 | 18 | 23 | 20 | 15 |
| 2 | 22 | 17 | 25 | 36 |
| 3 | 24 | 21 | 19 | 28 |
| 4 | 21 | 22 | 17 | 20 |
| Demand | 40 | 20 | 25 | |
- Explain why it is necessary to add a dummy demand point.
- Add a dummy demand point and appropriate values to Table 1 in the answer book.
- Use the north-west corner method to obtain a possible solution.
After one iteration of the stepping-stone method the table becomes
- Taking D3 as the entering cell, use the stepping-stone method twice to obtain an improved solution. You must make your method clear by stating your shadow costs, improvement indices, routes, entering cells and exiting cells.
- Determine whether your solution from (d) is optimal. Justify your answer.