2. Table 1 shows the cost, in pounds, of transporting one unit of stock from each of three supply points, \(\mathrm { A } , \mathrm { B }\) and C , to each of four demand points, 1, 2, 3 and 4 . It also shows the stock held at each supply point and the stock required at each demand point. A minimum cost solution is required.
\begin{table}[h]
| 1 | 2 | 3 | 4 | Supply |
| A | 17 | 20 | 23 | 14 | 25 |
| B | 16 | 15 | 19 | 22 | 29 |
| C | 19 | 14 | 11 | 15 | 32 |
| Demand | 28 | 17 | 23 | 18 | |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
Table 2 shows an initial solution given by the north-west corner method.
\begin{table}[h]
| 1 | 2 | 3 | 4 |
| \(A\) | 25 | | | |
| \(B\) | 3 | 17 | 9 | |
| \(C\) | | | 14 | 18 |
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{table}
- Taking A4 as the entering cell, use the stepping-stone method to find an improved solution. Make your route clear.
- Taking the most negative improvement index to indicate the entering cell, use the stepping-stone method once to obtain an improved solution. You must make your method clear by stating your shadow costs, improvement indices, route, entering cell and exiting cell.
- Determine whether your current solution is optimal, giving a reason for your answer.
- State the cost of your current solution.