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.

1. This is a balanced problem. Explain what this means.
2. Use the north west corner method to obtain a possible solution.
3. 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.
4. 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.
5. State the cost of the solution you found in part (d).