3. The table below 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 four sales points, \(\mathrm { P } , \mathrm { Q } , \mathrm { R }\) and S . It also shows the number of units held at each supply point and the number of units required at each sales point. A minimum cost solution is required.

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