2. The table shows the cost, in pounds, of transporting one unit of stock from each of four supply points, \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D , to each of three demand points, 1, 2 and 3 . It also shows the stock held at each supply point and the stock required at each demand point. A minimum cost solution is required.

1. Use the north-west corner method to obtain an initial solution.
   (1)
2. Taking D1 as the entering cell, use the stepping stone method to find an improved solution. Make your route clear.
   (2)
3. Perform one further iteration of the stepping stone method to obtain an improved solution. You must make your method clear by stating your shadow costs, improvement indices, route, entering cell and exiting cell.
4. Determine whether your current solution is optimal, giving a reason for your answer.