6. The table below shows the cost, in pounds, of transporting one unit of stock from each of three supply points, \(\mathrm { X } , \mathrm { Y }\) and Z to three demand points, \(\mathrm { A } , \mathrm { B }\) and C . It also shows the stock held at each supply point and the stock required at each demand point.
| \(\mathbf { A }\) | \(\mathbf { B }\) | \(\mathbf { C }\) | Supply |
| \(\mathbf { X }\) | 17 | 8 | 7 | 22 |
| \(\mathbf { Y }\) | 16 | 12 | 15 | 17 |
| \(\mathbf { Z }\) | 6 | 10 | 9 | 15 |
| Demand | 16 | 15 | 23 | |
- This is a balanced problem. Explain what this means.
- Use the north west corner method to obtain a possible solution.
- Taking ZA as the entering cell, use the stepping-stone method to find an improved solution. Make your route clear and state your exiting cell.
- Perform one more iteration of the stepping-stone method to find a further improved solution. You must make your shadow costs, improvement indices, entering cell, exiting cell and route clear.
- State the cost of the solution you found in part (d).