- Table 1 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 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 to this transportation problem is required.
\begin{table}[h]
| 1 | 2 | 3 | 4 | Supply |
| A | 24 | 32 | 21 | 34 | 27 |
| B | 28 | 31 | 29 | 37 | 41 |
| C | 25 | 41 | 33 | 35 | 31 |
| D | 23 | 32 | 31 | 36 | 14 |
| Demand | 33 | 35 | 25 | 20 | |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
Table 2 shows an initial solution given by the north-west corner method.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{table}
- Explain why a zero has been placed in cell C 2 in Table 2. State the other cell in Table 2 in which the zero could have been placed.
- State the shadow costs clearly and enter the improvement indices into Table 3 in your answer book.
Taking the most negative improvement index to indicate the entering cell,
[0pt] - list the stepping-stone route that should be used to obtain the next solution. You should make clear the cells that are included in your route and state your entering and exiting cells. [You do not need to state the next solution. You do not need to solve this problem.]